Caution: potential spoilers.
Eve of the Daleks, on BBC One (UK) / BBC America (USA)
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This is the first of three specials airing after series 13. It's also 2022's New Year's special. (It aired on January 1, 2022, but I didn't see it until May 2023.) On New Year's Eve, 2021, a man named Nick goes to a self-storage facility, which is run by a woman named Sarah, on whom he has a rather obvious crush (though she's totally oblivious to this, and just annoyed to be working on the holiday). Meanwhile, on the TARDIS, the Doctor has prepared an emergency reset to fix damage caused by the Flux (as seen in series 13). She, Yaz, and Dan must leave the TARDIS during the reset, and they unexpectedly show up at the storage facility, which is soon invaded by a Dalek. The Dalek kills Nick and Sarah, and then also kills the Doctor and her friends. But it turns out there's a time loop, so everything starts over. Eventually more Daleks appear, and they keep killing everyone, but each time they do, circumstances reset... though the Doctor realizes each time it happens, they have one minute less. Together, they must learn from each iteration of the scenario to ultimately defeat the Daleks.
Well, I thought it was basically an enjoyable story, with good guest characters. There's also an important revelation, when Dan talks to Yaz about her feelings for the Doctor. I thought that was a good scene, though I was kind of upset with Dan when he later told the Doctor how Yaz feels, which I don't think was his place to do. But the Doctor pretends she doesn't understand what he's talking about, and seems determined to just ignore the situation. Which is also problematic, on her part, I'd say. But maybe she's just waiting for Yaz to bring it up herself. I don't know. The Doctor is also still avoiding talking to Yaz about... other things, which she had promised to do. But I expect she'll get around to it when she's ready. (The Doc still has an awful lot to process about her own past.) Anyway, not sure what else to say. I'm not sure everything about the time loop made sense, and it's not the best time loop story the show has ever done, but it was still good.
Legend of the Sea Devils
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streaming sites: Amazon; Google Play; Vudu
This aired on Easter in 2022, but I didn't see it until July 2023. It's set in China in 1807, when a pirate captain named Madame Ching unwittingly releases a Sea Devil that had been turned to stone long ago. (The Sea Devils are a race that the Doctor had encountered before in the original series, but I don't remember whether or not I ever saw them before this special.) The Sea Devil kills a number of people in the village, including the father of a young man named Ying Ki, who blames Ching for his father's death. Soon after that, the Doctor, Yaz, and Dan show up. And the Sea Devil leaves on a flying sailing ship. Ching is trying to find a lost treasure which centuries earlier had been held by a captain named Ji-Hun, while the Sea Devil wants to find a powerful gem. And eventually the Sea Devils put the whole world in danger, in a way I don't want to reveal.
Well, I guess that's all I want to say about the main plot. I thought it was a decent story, and the main Sea Devil was a decent villain (who of course saw all of humanity as the villains). I thought Madame Ching was fairly cool. And we get to see the Doctor talk to Yaz about Yaz's feelings for her, which the Doctor would like to reciprocate, but feels she can't, because of... reasons. I don't want to say too much about that, but the special gets a couple of good scenes out of it. It's all very bittersweet.
tek's rating: 
¾
The Power of the Doctor
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streaming sites: Amazon; Google Play; Vudu
This serves as a "centenary special" for the 100th anniversary of the BBC. It begins with the Doctor, Yaz, and Dan trying to stop a space train robbery by CyberMasters. They fail. But it ties into a much larger plan orchestrated by the Master, involving both Cybermen and Daleks. After the train thing, Dan decides to end his time with the Doctor, because he nearly died. However, the Doctor and Yaz will have help from a couple of former Companions from the classic era: Ace and Tegan. They've been recruited by Kate Stewart as freelancers to work with UNIT. That's in 2022, but there's also a situation in 1916 that has to be dealt with. I don't want to spoil any details of the adventure, but of course the Master's plan is foiled in the end. Alas, he managed to wound the Doctor badly enough to trigger a regeneration, though before it takes effect she spends some time with Yaz before dropping her off on Earth. There, Yaz finds that Graham has started a support group for former Companions.
Meanwhile, the Doctor's regeneration into the fourteenth Doctor is a surprise, considering the identity of the next actor to portray the Doctor had already been revealed... and the one she regenerates into isn't him. It's practically unthinkable to me that anyone wouldn't have learned who it was even if, like me, they didn't see this special until well after it aired (I'm about a year late). But still, I won't spoil it until I review the upcoming 2023 specials. (I'm sure by the end of those, the Doctor will regenerate again, into the previously announced actor.) Anyway, I loved this special in every way, and found it a fitting send-off for the thirteenth Doctor and her Companions.