Spoilers will take the bus.
Anime movies are a rare breed. Sometimes they take their characters out of the timeline and set them upon an adventure that almost feels like it happens in an alternate reality. Sometimes the characters are unrecognizable or are simply completely new characters in a supposedly similar adventure or world. I’m glad to report this is very much a firmly rooted sequel to the end of the first season of Demon Slayer (Kimetsu No Yaiba). How essential to the main story this plot is, I cannot say. You’re pretty much watching a long episode straight out of the anime.

Demon Slayer (Kimetsu no Yaiba): Mugen Train (2020) was directed by Haruo Sotozaki. Following the events of the finale of the first season, Tanjiro, Nezuko, Zenitsu and Inosuke board a train. In this train, they are to meet the Flame Hashira, Kyojuro Rengoku. This won’t be a peaceful trip as a demon known as Enmu, Lower Rank One of the Twelve Kizuki, has sinister plans for them.
That’s as far as I will give out the plot, since what we get is basically a typical adventure that benefits from the extended format. I will say during the first act we get dream sequences cleverly inserted as plot devices. Tanjiro’s is specially both traumatic and cathartic as he re-encounters his family. Kyojuro’s dream sequences is a way to introduce the character and they also add some gravitas further on. Zenitsu and Inosuke are mostly here for comedic relief and their dream sequences follow that trend.
Actually most of the action centers around Tanjiro and Kyojuro. We do get some short sequences for Nezuko but she doesn’t have any character development of note. The battles are visually impressive, but there’s no particular heart-stopping moments like in the anime series. They are of comparable quality, but nothing like that unleash moment back in episode 19: “Hinokami”. Tanjiro does bring up the kagura dance with Kyojuro, though.
Only recommended for fans of the anime. It does play like a longer special of the anime series. I know it’s mandatory viewing if you’ve seen the show, but it does have some moments in which the comedy or the drama is drawn out a little too long. It might be a matter of personal taste, but it does seem to go for the heart strings with some excessive force. This makes the ending somewhat sour, and the future lives of our protagonists seem dark. That being said, your mileage might vary.
That will do for now.