A puppet drama that tells a story about the mundanity, isolation, and loneliness of life. It's does some neat things at the end that make really good use of the medium, but the poor pacing and the disrespectful of the viewer's time over the 90 minutes makes this hard to recommend.
So I'm just going to spoil it.
The movie starts with the same group of male voices talking, laughing, and ends the same way. Michael Stone is off to Cincinnati to give a speech about his book. Everyone sounds the same to him, his wife, his son, his old girlfriend, everyone in the world is voiced by the same male dude. They all have the same boring male face. But in the middle of the movie, he hears Lisa. A female voice!
He searches frantically and finds her. He eventually gets her to his room, where it's revealed that her face is different too. He admires even the dis-figuration on her face, because it's different from the same boring face everyone else has. They have awkward conversations, sing, then sleep together. He names her Anomalisa because she's an anomaly and her name is Lisa.
In the middle of the night, Michael has a nightmare that everyone in the world is the same person. Same voice, same face, they're all in love with him and hate Lisa for being different. He stays at the Fregolli Hotel named after the Fregoli Delusion which is the delusion that different people are the same person in disguise.
He wakes up, tells Lisa he's in love with her, he wants to leave his wife and kid and yadda yadda. In this sense, the movie does an amazing job at capturing the spark that happens when you meet someone intriguing for the first time. But then during breakfast, he becomes irritated with her because she'd talk with food in her mouth. Then as she talks about the same boring conversations that other people talk about, her voice started to change into the same male voice.
It skips ahead to the speech he gives. He's going through a breakdown and talks about how alone he is and how he has no one to talk to. The camera pans to the audience and Lisa now has the male face that everyone else has (I didn't notice this, I had to read about it later). So he goes home to his family, and his wife and ungrateful son are throwing him a surprise party. But he doesn't recognize anyone, and he asks who they are, and who she is. And his wife gets angry and counters "who are you?! who is anyone?!"
In the epilogue, we see Lisa driving home with her friend. Lisa's face is back to normal and she's writing a letter to Michael in her normal voice. At the end, the camera focuses on Lisa's friend, who also has a unique face that wasn't previously seen. So whatever is going on with Michael is all in his mind.
Again, the movie does an amazing job of making use of the medium to convey something from the human condition. I initially countered the male voices as being just a cost saving measure. (I didn't notice the same facedness of everyone). But they waste too much time establishing how mundane life is, something we're all too familiar with. The 90 minute movie probably could have been a tight 30.