Timeless, on NBC
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Caution: spoilers.

Season One
An alleged terrorist named Garcia Flynn (Goran Visnjic, whom I know from Extant) and his associates steal a time machine (called "the Mothership"), which was invented by a rich and famous scientist named Connor Mason. They also take with them a scientist named Anthony Bruhl (Matt Frewer), a member of Mason's team on the time machine project. At first, it's assumed that Flynn kidnapped him, as they needed him to pilot the Mothership. However, in later episodes it will be discovered that Bruhl is working with Flynn's group willingly, even if reluctantly. Meanwhile, following the theft of the Mothership, a few people are recruited to chase Flynn through time. They include a historian named Lucy Preston, a soldier named Master Sergeant Wyatt Logan (whose wife, Jessica, died four years ago); and a computer scientist named Rufus Carlin (Malcolm Barrett, whom I know from Better Off Ted). The three of them use a prototype time machine called the Lifeboat to chase Flynn into the past and try to stop him from changing history... though exactly how and why he wants to change any particular event are somewhat unpredictable, at first.

Well, Mason forces Rufus to secretly make audio recordings of what happens on his missions with Lucy and Wyatt. We eventually learn this is because Mason is involved with a sort of secret society called Rittenhouse. We also learn that what Flynn is trying to do by changing history is to weaken Rittenhouse's control over... pretty much everything that's happened in America since before America was a country. His reason for wanting to destroy the organization is that Rittenhouse was responsible for the deaths of his wife and daughter, for which he himself was blamed. However, stopping Rittenhouse also means doing a lot of harm to history. And the team that's trying to stop Flynn may have to question whether they're even on the right side. Things get more complicated when various secrets come out, like the fact that Flynn has a journal ostensibly written by Lucy sometime in the future, when he says she'll be on his side. And it further divides the team when Wyatt and Lucy learn that Rufus had been recording them. But ultimately, the three of them remain on each other's side, whether or not they can trust anyone else. Meanwhile, the Department of Homeland Security has a special agent named Denise Christopher presiding over the whole operation at Mason Industries, and she eventually begins investigating Rittenhouse. There's also a programmer at Mason Industries named Jiya, who develops a romantic relationship with Rufus. Oh, and Mason himself doesn't seem to be all that happy about his own involvement with Rittenhouse, so it's unclear whose side he'll ultimately land on.

On a more personal front, in the pilot episode, changing the past changed Lucy's present in some very unexpected ways. Her mother, Carol (Susanna Thompson, whom I know from Voyager and Arrow), had been dying of cancer, but upon the Time Team's return to the present, Lucy finds that her mother is perfectly healthy. Which seems good, but it also turns out that Lucy's sister Amy never existed. So it takes awhile to figure out how that happened, and of course Lucy very much wants to get Amy back. Also, Lucy is now engaged to a man named Noah, whom she's never met. So she does her best to avoid him, while not letting him know why she's avoiding him. (Because of course, the whole time travel thing is top secret.) Meanwhile, Wyatt hopes that somehow their time traveling could give him a chance to save his late wife's life, regardless of the rules against changing history. And eventually, we learn that a former Mason Industries time machine pilot named Emma Whitmore has been hiding from Rittenhouse in the 19th century for some time now. But she ends up joining Flynn's team. Subsequently, Anthony Bruhl turns against Flynn, who ends up killing him. So from then on, Emma is Flynn's pilot. Also, Jiya begins training to become a time pilot, as a possible replacement for Rufus.

And... there are a few surprises I'll avoid spoiling for now. Meanwhile, it's been fun seeing a bunch of famous historical figures, and whatnot. And I guess that's all I can say, for now.

Season Two
So... last season, after traveling back in time, Jiya had a seizure... and a prophetic vision. These seizures and visions become an important aspect of this season. Also last season, the good guys managed to do a lot of damage to Rittenhouse in the present, but they didn't completely eliminate them. Flynn was arrested by the NSA. Meanwhile, Emma got away with the Mothership, and this season she works for Rittenhouse. Also last season, Lucy learned that her mother has been a member of Rittenhouse all along, and wants Lucy to join the organization, herself.

At the start of season two, Mason Industries is bombed, so the team relocates to a secret bunker. Also, Mason loses his money and apparently the respect of the scientific community. Lucy is working with her mother and Emma, though not willingly. And it's not long before she's reunited with her friends, so they can work together against Rittenhouse. They learn that the organization has sleeper agents at various points in history. And Rittenhouse brings a soldier named Nicholas Keynes from 1918 to 2018. Carol reveals that she is his granddaughter, and that Rittenhouse has been following his plans. Now she wants him to lead the organization in the present. Also this season, the Time Team gets a bit of information from Flynn to help them against Rittenhouse. And eventually, they help him break out of prison to join their team full time, though none of them really trust him. At one point, Lucy and Wyatt begin a romantic relationship. But shortly thereafter, Wyatt learns that Jessica is alive, but with different memories of their relationship than his own. Things hadn't been going well between them, in her new timeline, but he gets her to give him another chance by taking her to the bunker and revealing the truth about time travel. (It's presumed that Rittenhouse must be responsible for her being alive, though why they would have saved her remains a mystery, for most of the season.) So, there is some tension between Wyatt and Lucy, who go back to being just friends. And at one point, Jiya has a vision of Rufus being killed, and wants to try to prevent that. Meanwhile, of course there are lots of interesting missions throughout the season, where the team meet various famous people (and in one episode, they meet a younger version of Agent Christopher).

The Miracle of Christmas
First I want to mention that the show was cancelled after the first season, but then very quickly and miraculously got renewed. It was cancelled again after the second season, and again had a miraculous renewal... though this time, only for a two-hour movie to wrap things up. (Some websites will include the movie in season two, referring to it as two episodes, "The Miracle of Christmas parts 1 and 2." But it isn't really part of any season.) Anyway, the movie aired on December 20, 2018, and it's set around Christmas both in the present and in one of the historical eras the Time Team goes back to. Now, I need to mention that at the end of season two, Jiya became stranded in 1888... well, actually, 1885, but the Time Team only discovered a photo of her in 1888, which is when they went back to get her. But by then, she'd been living in the past for three years. She didn't want to go with them, because she knew from her vision that it would lead to Rufus's death. But... Rufus ends up being killed by Emma (rather than her henchmen, as in Jiya's original vision). Emma also kills Carol and Nicholas, and becomes the new leader of Rittenhouse. It's also discovered that Jessica has been working for Rittenhouse all along. The season ended with an upgraded Lifeboat appearing in the bunker. Future versions of Lucy and Wyatt emerged, asking their younger selves if they want to save Rufus. So that was pretty cool, and of course made it feel like there absolutely had to be a follow-up. And now there is....

So, the future Wyatt and Lucy give their present selves Lucy's journal and their Lifeboat, then take off in the older Lifeboat. (I'm not sure what happens to them; I suppose we're meant to think they are erased from existence when their younger selves change things, but it seems to me that since they had a time machine, they might have been spared erasure. Maybe I'm wrong. It doesn't really matter, for now.) Anyway, the Time Team take the new Lifeboat to 1848, to thwart Rittenhouse's latest plan, before they even have a chance to do anything about Rufus. However, Flynn makes a solo trip to another time, where he makes a sacrifice that changes the timeline, so Rufus never died. The team later makes another trip, this time to Christmas Eve, 1950, in North Korea. Meanwhile, in the present, Mason and Christopher discover that their friends died in 1950, so they come up with a plan to save them. After everyone returns to 2018 and celebrates Christmas, we see a flashforward to 2023, and the Time Team makes one brief, final trip to the past. Well... I'm leaving out lots of details, but the movie has plenty of drama and humor and all kinds of feels. Various sacrifices are made, which seem sad, but necessary. And basically, all the plot threads are neatly wrapped up, and we see that our heroes have happy lives in the future. There's also a hint that they might someday need to go back to time traveling again for all new reasons, but... that's open-ended. The present story, however, is complete, and I found it a very satisfying ending to the series.