It’s remarkable, or remarkably annoying anyway, that Will Smith seems to have aged hardly any at all in the 15 years between the original Men in Black in 1997 and this second sequel, which is itself remarkable for being better than either of its predecessors. Like them it’s not a great film, but it’s a decent comedy, a fairly good adventure film, and even touching in places.
The plot involves an alien villain, one looking something like a mutant biker, who manages to kill Tommy Lee Jones’s character in the past, so that no one besides Will Smith remembers him. And it’s good that he does, because without something Jones did, or should have done, in 1969, all humanity is in danger of being wiped out by an alien enemy. The only solution is for Smith to time-travel back to the 1960s, following the villain’s lead, and fix the problem. In the course of this he runs into the younger version of Tommy Lee Jones’s character, and the two of them wind up at the launch of Apollo 11.
Josh Brolin does an excellent and very entertaining job of playing young Tommy Lee Jones, even though he’s about 20 years older than Tommy Lee Jones was in the 1960s. (At one point Will Smith observes, “You got some city miles on you.”)
A curious bit of trivia: At one point, during a visit to an alien-run Chinese restaurant, we see a fish with a cartoonishly human-like face that might be the single most unbelievable thing in the movie. But weirdly enough, this creepy thing is a real fish found in deep water in the neighborhood of Australia and is aptly called the blobfish. It’s facing extinction because it's often caught by boats bottom trawling for crabs, lobsters, and the like, even though the blobfish itself is considered inedible. Here's a YouTube video with several photos of them in real life. At least one of the "facts" asserted seems doubtful to me, by the way. Surely blobfish have at least some muscles (a heart, for example, and some muscles for swimming and digestion), even if they don't exactly work out (not that I'm one to talk).
I don’t want to say more about MiB 3 to avoid spoiling your enjoyment (though I might have done that by linking to the blobfish video). If you at all liked either of the previous Men in Black films, you should see this one.