This film knew how to honor and equal the first film.
Despite their popularity, the first two MIB films, from the turn of the century, are films I don't really like to watch. The first movie, from 1997, is still worth it, but the second one was so bad that they had to wait more than ten years for this movie to come out, and even then, we still remember it. Good news: this movie is virtually as good as the first one and knows how to meet the public's expectations.
The plot is reasonably simple, but it guarantees entertainment: over the years, the boss of the MIB organization became a woman. Meanwhile, the escape of a dangerous alien from the lunar prison will force J to travel back in time, to the beginning of K's career, to try to prevent planet Earth from being invaded by a destructive galactic force. The script does a reasonably effective job and there is a lot of movement and action.
Will Smith shows that he has matured as an actor, and he knew how to imprint that maturity on the MIB agent he played: J is no longer a rookie or someone who accepts lessons, he is a senior agent with experience, who knows what he is doing and is sufficiently trained to deal with what you have in hand. Of course, K remains a veteran, and Tommy Lee Jones won't let that go by the wayside: sullen and seemingly unflappable, Jones' character will take particular pleasure in lecturing and lecturing Smith whenever appropriate. And, ultimately, it's the way the two actors interact that makes the movie funnier. The villain is worthy of our dislike and has some good jokes and tongue-in-cheek lines, but Jemaine Clement seems to have sometimes exaggerated things a bit. Michael Stuhlbarg and Josh Brolin do a very honest and committed job, and they help substantially to increase the quality of the film.
Technically, there is a serious and substantial bet on CGI, computerization and computer-made effects. It's something almost predictable, nowadays it's a very widespread resource and sci-fi or action movies have learned to master it. However, the authenticity of real scenes always tastes good. So the ending seems to be a bit out of step with the rest of the movie, but that turns out to be a minor problem. The cinematography is quite well executed, the sound and soundtrack are effective, the visuals as well. The sets and wardrobe, as well as the props, are in line with what you would expect to find in a MIB film.