The Animatrix

Optional, and it contains the single best piece of Matrix material outside the first film. Nine shorts from nine sets of hands, including Shinichiro Watanabe, Peter Chung and Koji Morimoto, written or overseen by the Wachowskis and made alongside the sequels rather than after them.

The two-part "Second Renaissance" is the reason to watch. It tells how the machines won: a robot kills a man who was about to decommission him, a legal case goes against the machines, their city is destroyed, and humanity darkens the sky rather than surrender. It is told as a history lesson with no protagonist, and it is bleak in a way the films never attempt, because humans are plainly the aggressors in it. The films gesture at this backstory in a line or two. This makes you watch it happen.

Placement matters more here than anywhere else in the series. Chronologically it is first by more than a century, and the in-universe toggle on this site puts it there. Do not watch it first. The shorts assume you know what the Matrix is and what is at stake in leaving it, and "Second Renaissance" lands as a gut punch only once you have seen what the machines built afterwards.

One short has a direct function: "Final Flight of the Osiris" ends with the crew delivering the warning that Zion's forces act on at the start of Reloaded, so it is the connective tissue between the first and second films. The others range from excellent to slight. "Beyond" and "Program" are worth your time; a couple are forgettable.