Spoilers from here on in.So we start off on a Russian submarine in 1983. They are preparing for nuclear war until the scientist enters, singing. Twist, it was just a drill. We are then introduced to the stupidest character ever. Also, the character who should get blamed for everyone else's near demise. Some dumb sailor decides that he can't wait until they get to Moscow, he wants to melt the giant ice block that has a mysterious creature in it NOW. I bet this guy always peeked at his birthday presents ahead of time. Anyway an Ice Warrior pops out and immediately makes this guy regret melting him out. Also the sub starts sinking.
The Doctor chooses this moment to prove that he reall?y has no right to make promises to get people back to a certain place by a certain time by appearing on the sub shouting "Viva Las Vegas". He manages to stop the sub from sinking by getting it to land on an underwater shelf. During all this the TARDIS disappears. I liked how the Doctor basically ignored any attempt Clara made to ask what happened to it. Also, I actually really liked how the used Clara hitting her head as a way to move the story forward to a point where the Doctor and Clara can talk with the crew. I also liked when they got frisked and the Doctor asked for a receipt.
Anywho, the Ice Warrior pops up, and it turns out the Doctor knows him. This is not good news. Proving that IQ tests aren't given to the members of the sub's crew someone shocks the Ice Warrior (named Skaldak), who up until that point hadn't hurt anyone who didn't deserve it, and who was being nice and chatting with them. He goes down. Clara tricks the Doctor into explaining that the Ice Warriors are from Mars and that the armor doesn't adjust well to temperature changes.
Someone needs to go beg for forgiveness and since Clara is the only non-warrior, she volunteers. Unfortunately, Skaldak a) knows that she's being told what to say and b) isn't in the armor that Clara was talking to. This is very, very bad. There was a very good moment when Skaladak sent out an unanswered signal to his people, and another where he mourned the loss of his daughter, who presumably died in the 5,000 years he was in the ice. Skaldak kills some people and Clara asks the Doctor to grade her on her performance. During this sequence while everyone is running around, Clara proves how different she is from every other companion (except Brian). When the Doctor tells her to stay, she does without argument. She does not wander off. Also, she learns about the TARDIS translation matrix when she finds out that she is somehow speaking Russian. Did she just assume that everyone but the barking alien was speaking English, despite being another planet and in the future last week?
Anyway, there's some nice metaphorical stuff about the Cold War and Mutually Assured Destruction. The Doctor gets Skaldak to stand down a little by asking him to show mercy. Also, he threatens to blow up the submarine they are all on.
In what was certainly not a deus ex machina, it turns out that Skaldak isn't the last of his kind. The sub is lifted up by a tractor beam from an Ice Warrior ship. Skaladak goes with his people, and disarms the submarine. Happy ending. Except for one minor detail. Where's the TARDIS?
Turns out there's a system called HADS (Hostile Action Displacement System) that moved it to safety. Specifically, the pole. The South one. He asks for a lift from the submarine crew. If they end up turning him down, I'm sure he can just ask UNIT though.