Lucifer, on FOX (s1-3) / Netflix (s4-6)
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Caution: spoilers.

Season One
This is apparently based on a character from comic books that I haven't read. But it's really not important to know anything about that, because basically it's just about the Devil, and of course he's had countless other fictional incarnations. So it shouldn't be hard to figure out what's going on. Anyway... sometime prior to the start of the series, Lucifer Morningstar decided to take a "vacation" from his duties as lord of Hell. Now he runs a nightclub in Los Angeles called Lux, where a demon named Mazikeen (Maze) works as a bartender (she's also Lucifer's bodyguard). At the start of the series, someone Lucifer once helped gets murdered, and he decides to investigate. This means tagging along with a police detective named Chloe Decker, who isn't happy about his presence, but she can't get him to stop butting in. And he does prove somewhat helpful, because he has a power to compel people to reveal their deepest desires (among other powers). However, Chloe herself is immune to this power, a fact which intrigues Lucifer. So even after the murder from the first episode is solved, he'll keep getting involved in her cases. And he doesn't even hide the fact that he's the Devil, but Chloe refuses to believe it. Still, she becomes increasingly curious about how he does some of the things he does, so I'm not sure how long she'll continue to doubt the truth. (Eventually, he convinces her to shoot him, to prove he can't be hurt. But he does get hurt, which confuses him. For several episodes, he believes he's lost his invulnerability, but he eventually realizes he's only vulnerable when he's near Chloe. The reason for this remains a mystery, for now.)

Meanwhile, there are some other characters I should mention. Chloe's ex-husband, Dan Espinoza, is also a police detective. And they have a young daughter named Trixie (Wikipedia says her real name is Beatrice, but I don't remember hearing that on the show; it may be info taken from the comics). She takes an immediate liking to Lucifer, though he dislikes children (but I think he may dislike her less than most kids). There's also an angel named Amenadiel, who keeps showing up and urging Lucifer to return to Hell, which Lucifer refuses to do. They really seem to dislike each other, though they're actually brothers, and their relationship is... complicated. Apparently, Amenadiel has been placed in charge of Hell in Lucifer's absence, and it's not a position he enjoys (for obvious reasons). Anyway, both Amenadiel and Mazikeen think Lucifer is going soft, ever since he came to Earth. In the past, he only cared about punishing the guilty, but now he's starting to care about humans, and wants to get justice for those who have been wronged. (Of course, his idea of justice is considerably different from Chloe's, which can lead to more problems between them.) Also, in the course of their first case, they met a psychiatrist named Linda Martin, who becomes Lucifer's therapist and lover. (Though after awhile, she puts an end to the latter role, because it was unprofessional.)

Throughout the first season, there are references to a case Chloe had been working sometime prior, in which she believed a cop named Malcolm Graham was dirty. He ended up getting shot under mysterious circumstances, and he's in a coma for the early part of the season. Now most of the cops in Chloe's precinct are upset with her for the accusations she had made against him. But eventually he dies for a few seconds, and is then brought back to life by Amenadiel, who wants to use him against Lucifer. And it turns out Chloe was right about him. Also, at one point in the season, Maze tells Amenadiel about Lucifer's therapy sessions with Linda, so he starts pretending to be a therapist, and takes an office next to hers, to keep tabs on Lucifer. Meanwhile, Amenadiel and Linda soon develop a friendship. (But that is seemingly ruined when she eventually learns he's not a therapist.) Also at the end of the season, Malcolm frames Lucifer for murder, and Amenadiel realizes he'd made a mistake in bringing him back to life. So they team up to stop Malcolm, who is finally killed. But not before he kills Lucifer, who then makes a deal with his father (God). Lucifer returns to life, but from now on he'll be doing his father's bidding. The season ends with Lucifer telling Amenadiel that he has to return an escaped soul to Hell. (I won't reveal who that soul is until next season. And there's at least one other development I'll hold off on spoiling, for now.)

So far I find the show reasonably entertaining, mostly because of Lucifer has an amusing charisma (which is well served by his British accent). Aside from that, there are some interesting mysteries, like why Chloe isn't affected by Lucifer's powers (and why he's vulnerable around her).

Season Two
So, the story picks up like a couple days after last season, I guess. The escaped soul Lucifer has to capture is his own mother, whom God had sent to Hell a few thousand years after sending Lucifer to Hell. But she doesn't have a body of her own, so she has to possess a recently deceased body. She hops around between a couple of men's bodies (which are immediately re-killed), before claiming the body of a murdered woman named Charlotte Richards (Tricia Helfer), who was a managing partner in a law firm. Though actually, we don't see her until the very end of the season premiere, and don't see how Lucifer's mum acquired her current body until episode 2. (So far, we haven't heard an actual name for her, and at this point I'm not comfortable calling her "Charlotte." So for now, I'm going to do as Lucifer does, and refer to her as "Mum.") Anyway, at first Lucifer was worried that she wanted to kill him in revenge for all the years of torture she endured in Hell. Maze was in charge of that torture, and was disappointed at never having broken her. So she's eager to give it another try, now that the former Goddess is inhabiting a vulnerable human body. However, Lucifer learns that Mum doesn't want revenge, so he forbids Maze from hurting her. (Though Maze is still upset with Lucifer about something that happened last season, so she's not working at Lux anymore, I guess. Oh, and she eventually moves in with Chloe.) Mum also makes a surprising revelation to Lucifer, which I don't want to spoil, but it sort of helps him get over his resentment about her having supposedly done nothing to help him when his dad originally sent him to Hell. (However, it still seems as if she may have motives she's hiding from him.) Lucifer decides that instead of sending Mum back to Hell, he'll force her to remain on Earth, which she considers a punishment. She has to pretend to be Charlotte, which includes living with Charlotte's husband and kids and working at Charlotte's law firm (without anyone finding out she's not Charlotte).

Also this season, Dan has been demoted (following a ridiculously brief suspension), because of something that happened at the end of last season, which I don't want to spoil. So now Chloe is his superior. And there's a forensic scientist at the LAPD named Ella Lopez, who helps with Chloe's cases. She seems like a fun addition to the ensemble. Also, Dr. Linda is still upset with Amenadiel about having lied to her last season, which was a serious betrayal of the trust she'd placed in him. But he soon apologizes, and they restore their friendship. However, he seems to be starting to lose his angelic powers, for a reason that I don't think has yet been explained. And... Chloe is targeted for death by Lucifer and Amenadiel's brother, Uriel, which ultimately leads to Lucifer killing Uriel. (He uses a dagger which Uriel had gotten from Azrael, the angel of death, which Uriel had been going to use on Mum.) Naturally, killing his brother is pretty traumatic for Lucifer. He later reveals his true face to Linda, so she now knows he really is the Devil, and that's not just a metaphor. This leaves her terrified for awhile, of both Lucifer and Maze, but ultimately she gets over her shock and things sort of go back to normal between the doctor and the demons. Chloe learns that the man who had been convicted of killing her father, years ago, was innocent. The man behind his death was actually a prison warden named Perry Smith. Maze becomes a bounty hunter. Mum tries to kill Chloe, as part of her plan to get her sons to return to Heaven with her, but Amenadiel talks her out of that. Still, Lucifer has no desire to leave Earth, so Mum tries to find other ways to get him to change his mind, which includes defending Warden Smith in his murder trial. She wants to force Chloe to lie on the stand, but she doesn't... which results in Smith being found not guilty. Later, Amenadiel meets Chloe's mother, Penelope Decker (Rebecca De Mornay, first seen in a season 1 episode). He soon realizes he'd seen her thirty-five years ago, and... this leads to the show finally revealing what's special about Chloe. She's a "miracle," which is to say, her parents were unable to conceive naturally, so God had sent Amenadiel to... make it possible for them to conceive, I guess. I still don't know exactly what that means, except that it somehow explains why Chloe is immune to Lucifer's supernatural charm, and why he's vulnerable around her. Anyway, now that Amenadiel realizes Chloe is the product of that miracle from all those years ago, he tells Mum about it. And she starts making plans to use this information.

After a month-and-a-half hiatus, the show returns for a trilogy of episodes. Mum encourages Lucifer to pursue a relationship with Chloe, and things seem to be going well, until he learns the truth about Chloe's origins. It's something she herself is unaware of, and I don't get the impression that anyone's going to tell her. But Lucifer finds it disturbing, because it seems like her very existence could be part of his father's plan for him, and of course he wants no part of that. Meanwhile, there's a designer poison which has recently been smuggled into the city. We first see it in the first episode of the trilogy, though it's not until the second episode that we learn that it's a poison. And at the end of that episode, the person who created it (and its antidote) kills himself, after having poisoned Chloe with it. In the conclusion of the trilogy (which is the midseason finale), an antidote must be found to save Chloe's life. But the only way to do that turns out to be for Lucifer to kill himself, in order to return to Hell and question the poison's creator. So, that was pretty dramatic, to say the least. And when he has trouble returning from Hell, Mum goes to bring him back, and almost gets stuck there, herself. But before returning to Earth, Lucifer gets a clue from his own subconscious that something Uriel had said right before dying might have been more significant than he thought. Also, Amenadiel finally finds out that Linda knows the truth about Lucifer and Maze and him. And... Lucifer leaves town without telling anyone.

After a three month hiatus, the show returns... and just two weeks have passed, within the story. Lucifer returns to L.A., and he's married to a woman named Candy... or at least he pretends to be. But that ends after one episode. Um... then we learn that Azrael's dagger is actually one piece of the Flaming Sword. Lucifer has to ignite it, so he can cut through the gates of Heaven, but first he has to find the other pieces of the sword. He lets Mum think that he intends to return to Heaven with her and Amenadiel, but in fact he plans to lock them in there and return to Earth. Meanwhile, there's an episode involving a mental patient named God Johnson (Timothy Omundson), who believes he's actually God. It's a pretty interesting story, and it ends with the revelation that he'd changed his name from Earl and started believing he was God after buying a belt buckle that turns out to be the second piece of the sword. There's another episode where Mum tells Chloe that she's Lucifer's ex-stepmother, which kind of neatly explains away some of the weirdness of "Charlotte" getting involved in Lucifer's life. Also, it turns out that a necklace Amenadiel had been wearing all along is the third and final piece of the sword. Since it had been entrusted to him by his father, he assumes he's actually God's favorite son, a distinction he'd always thought was held by Lucifer. And he doesn't want to give the piece to Lucifer, because returning Mum to Heaven would incite a war between her and God, which could result in the deaths of many of their other children (Amenadiel and Lucifer's siblings who are still in Heaven). Meanwhile, Mum's powers have been increasing, and the body of Charlotte Richards won't be able to contain it much longer... and when it ceases to contain the Goddess's energy, a lot of innocent bystanders could die. But Lucifer discovers where Amenadiel had hidden the third piece, and completes the sword. He uses it to open a portal to... I guess another universe, or like, a dimension where there wasn't a universe. Or something. He sends Mum (that is, the energy within the borrowed body) through the portal, so she can create her own world, and not put anyone (humans or angels) in danger. After that, Charlotte wakes up with no memory of anything that happened since she died (which presumably means the Goddess's energy had brought her back to life, which surprised me- and Lucifer- because I assumed the body would just go back to being dead). Meanwhile, it seems like Amenadiel got at least some of his angelic power back. Also, Lucifer decides he'll finally reveal the whole truth about himself to Chloe, but before he can do so, he's knocked unconscious by someone. He later wakes up in the desert, and he has his wings back. (I don't think I mentioned that he'd cut off his wings... I think prior to the start of the series. And at one point in season one, he burned them, so it's very mysterious that it's even possible for them to be back on his... back... now.)

Season Three
The first thing I need to mention is that season two was originally meant to have 22 episodes, but was then cut to 18. However, the four episodes that were cut from season two were later added into season three. I thought they'd all happen at the start of the season, but that's not actually what happened. They end up becoming episodes 3, 6, 7, and 11. It's kind of awkward, and while I think some changes may have been made to the episodes in an effort to make them fit, storywise, within the timeline of season three, it's still not a perfect fit. (Then again, if I hadn't read about all this online, I might not even notice a problem.) In any event, the actual first episode of season three seems to me to pick up right after where season two left off, and I don't think it would have made sense for the events of the four shuffled episodes to take place between the season two finale and the season three premiere (though it's possible that without the changes that were made to them, or that might have been made to the season premiere, could have allowed everything to work out naturally). I dunno.

So... at the start of the season, Lucifer cuts off his new wings, but they grow back. I suppose this pattern happens several times, before he finally stops cutting them off. (Though of course they can still be hidden within him, so humans can't see them. Or whatever.) Also, he tries to show his true "devil face" to Chloe, but he's lost the ability to do so. And he learns about a mysterious crime boss called the "Sinnerman," whom he believes is responsible for regaining his wings and losing his devil face. So he wants to find the guy, but that will remain a mystery for now. Meanwhile, there's a new lieutenant at the LAPD named Marcus Pierce (played by Tom Welling, of Smallville fame), who becomes Chloe and Dan's new boss. He'd just been transferred from Chicago, where apparently he'd tangled with the Sinnerman, himself. Or something. So he knows the guy is dangerous, anyway. Also, the angelic powers Amenadiel had apparently gotten back at the end of season two vanished again, so he believes he's still being tested by God. There's an ep (the first of the four holdovers from season 2) that focuses on Maze's work as a bounty hunter, tracking down a fugitive named Ben Rivers, who turns out to be both charming and a pretty competent rival for Maze. And we eventually see Charlotte Richards again, working at her old job as a lawyer, but she has no memory of the events of her life during which she was possessed by the Goddess, which had resulted in her being separated from her husband and kids. So she's really freaked out about her missing time, and has been trying her best to pretend to remember it, so no one will think she's crazy. And it turns out she had been trapped in Hell during that time, and she's desperate to change her ways so she won't ever go back there. And in the second holdover episode, Lucifer and Ella go to Las Vegas to help Lucifer's ex-wife Candy when it turns out she's in danger. In the third holdover, an investigative journalist named Reese Getty, who turns out to be Linda's estranged husband, learns that Lucifer is the Devil. But this is partially a flashback episode, so it takes place mostly prior to Linda herself learning the truth. So when he tries to convince her, he just seems crazy. (Of course, the fact that he refused to accept that their relationship was over did a fair job of that, on its own.) I don't want to reveal any more of the plot of that episode, but it ends with a twist. (I really thought he'd turn out to be the Sinnerman, but he didn't.) Eventually, Charlotte leaves her law practice, to stop defending people she knows are guilty, and instead joins the District Attorney's office. She also tries to learn to be "good" from Ella, who just wants to avoid her, because she finds Charlotte scary. The Sinnerman is eventually caught, but Lucifer fails to get all the answers from him that he wants, before he's killed. However, it does seem that the Sinnerman was just working for someone even more powerful. (Or maybe that even more powerful person is the real Sinnerman. Whatever.) Also, Lucifer discovers that Lt. Pierce is actually Cain, of Biblical fame. And the final holdover episode is entirely a flashback to 2011 (five years before the start of the series), when Lucifer first came to L.A. for a vacation (having previously come to Earth numerous times over the millennia for similar vacations), but ended up deciding to stay there permanently. The episode also shows us how Chloe worked towards becoming a detective (including a brief meeting with Charlotte Richards), why Lucifer brought Mazikeen to Earth, how he got Amenadiel to let him stay on Earth, and how he originally removed his wings.

Well, it turns out that Pierce/Cain really wants to die, and considers his immortality a curse from God for killing his brother, millennia ago. So Lucifer agrees to help find a way to kill him. Also, Linda starts dating Amenadiel, but they keep it secret from Maze, who they know wouldn't be comfortable with the idea. But Maze eventually finds out about the relationship, and is furious at their deception. And even Linda breaking up with Amenadiel for the sake of her friendship with Maze doesn't make Maze any less angry. Rather, she cuts ties with all her human friends, and moves out of Chloe's place. She wants Lucifer to return her to Hell, but he refuses. So she eventually teams up with Pierce in a scheme to get what they both want. Meanwhile, Pierce starts dating Chloe, which makes Lucifer jealous. And Dan starts a relationship with Charlotte. And Lucifer tells Charlotte the truth about his mother having possessed her, and everything, so she'll stop thinking she's going insane.

And... lots of other stuff happens, including some major plot developments that I'm not going to spoil. I will say that the way the season ends, it seems like the next season would be quite interesting. Unfortunately, the show moved from FOX to Netflix, which I don't get. It ran for another three seasons there.