The Doctor regenerates into the form of Peter Capaldi! Companion Clara Oswald has to help him get reoriented while he helps her go on fantastic adventures, not only in space and time but in her personal life as well. She's settled in to a teaching job. The school provides both a place for action and a new boyfriend for Clara in the form of Mr. Pink--ex-military, now maths teacher. The series follows the usual formula of mixing some Earth history, some Earth present day, and some other worlds into the show while giving some hints at the big finale and a romantic interest for the companion (though thankfully the romantic interest is not the Doctor!).
I like Peter Capaldi as the Doctor quite a bit. He has a good mixture of zany franticness with occasional seriousness and grumpiness that makes his Doctor charming. Jenna Coleman as Clara does a good acting job but the writing for her character is all over the place. Sometimes she's sweet and fun, sometimes she's bossy and taciturn, with little narrative to give her character continuity. Her love interest, Mr. Pink, does not have quite enough depth to make him a very interesting character.
Overall, I've found the writing to be substandard this year. In addition to the variable nature of Clara's character, a lot of the stories are either not compelling or so full of plot holes as to be distracting. The overarching theme questioning whether the Doctor is a good man/hero also feels a bit forced and unsatisfying, especially with the "I'm just a guy running around having adventures" conclusion. The theme could have been inspiring and challenging, but it comes off like a rehash of previous series (like those last few David Tennant episodes) with no decisive or compelling ending.
I haven't seen the Christmas episode but am definitely going to wait until it's available from the library or free streaming somewhere. Oh Doctor, what's happened to you?