Let's be blunt. I reckon 2001 is among the most over-rated films in cinematic history. Large sections are extremely tedious, it's certainly hideously overlong, and the climax attempts to pass off incoherent, psychedelic mumbo-jumbo, instead actually finishing the script. This leaves the sequel with the task of having to try and make sense of its predecessor, as well as push its own story along, but the results are decent and - a real surprise - intelligible. It's based around a joint Soviet-American mission (the Russians having the hardware, the Yanks the expertise) to discover what happened to the last spaceship, culminating in Bowman's cryptic, "My god, it's full of stars."
Add in a Cuban missile-style crisis brewing on Earth, and there's plenty of scope for tension, inside and outside the craft. Mirren is surprisingly plausible as the Soviet commander, cautiously growing to trust Scheider, leader of the American group. They are ably supported by Balaban and Lithgow, who each get a starring sequence, the former persuading HAL 9000, the latter doing a spacewalk. And yes, Even HAL, the villain of the original, shows more depth than previously permitted, and becomes something of a hero. Visually, can't fault the picture much; the effects are perhaps a little gratuitous, but they are splendid, and have hardly dated - which is a lot more than can be said for the computers in the film, however... The ending is somewhat trite, but I'm perfectly happy to settle for that over Kubrick's mess.