In 1970, Elvis Presley met Richard Nixon. He arranged this simply by turning up and asking to see the president and by basically, you know, being Elvis.
Elvis and Nixon is an enjoyable, low key historical comedy/drama, documenting Elvis' campaign to get into the Oval Office and speculating on what passed between the President and the King. (Nixon had not yet begun recording his meetings, so there's no actual record of what was said.) The handwritten letter that Elvis wrote to Nixon is still around, and we know that Elvis basically wanted to be made a secret Federal Agent so as to save America from hippies.
The film works mainly because of excellent performances by the two main actors, Michael Shannon playing Elvis and Kevin Spacey as Nixon. These are damn tricky performances. After all, Elvis and Nixon have to me two of the most imitated men of their time, and yet Shannon and Spacey avoid doing straight out imitation. Yes they keep some of the mannerisms but they're more interested in getting to the humanity of their respective characters. This is very important, because the gap between the public and private faces of celebrities is a key theme of the movie.
It's also a hugely funny movie. It's not a comedy in the sense of being about set-ups and jokes, but about the basic absurdity of the entire situation. Some of the humour comes from the weird way in which two very different and yet very similar forms of power interact, overlap and contradict. Some of the other laughs come from the specific characters of Elvis and Nixon and the different ways in which these two leaders keep their subordinates in line.
Elvis and Nixon is an unusual thing in an American historical movie, steering away from the huge issues and explosions, working on a small scale. Taking place on one day in a handful of locations it nonetheless has an awful lot to say about an event which was not particularly important, and yet which manages to be deeply telling.