Sunday was International Moon Day (yes, that's a "thing") commemorating the date that human beings first put boot-treads on the Moon. That historic mission figured fictionally in this movie.
Written at the time of the film's release.
or
"Don't Ask Questions You Don't Want to Know the Answer To..."
The third "Men in Black" film had to go somewhere else but up. The first two films were variations on the "illegal alien" theme about a government organization that monitored the activities of extraterrestrials in the world and specifically New York City, and revolved around alien invasions and the containment of said aliens. And when you've seen one alien invasion directed by Barry Sonenfeld, you've seen them all, and hyper-kinetically at that. And once it's been established that "aliens can be anywhere" the joke runs a bit dry pretty quickly, especially when the sub-species can contain pug-dogs and large cockroaches. The second film tried to expand on those concepts and felt a bit thin in the process, concentrating a bit too much on the secondary characters rather than the basic plot and the character interactions.
So, where does Men in Black III go from there?
One of the nice aspects of the series has been its ability to still think outside the box, while expanding the horizons of just what that box might contain, be it variations of scale and dimension, even if only in afterthought. With the infinite reaches of space seemingly exhausted, the group (based, supposedly on an idea by Will Smith) has the series going back in time. Naturally. It ostensibly revolves around an Earth-takeover plot by another alien (one must ask at some point "why always us?"), "Boris the Animal" (who seems based on the DC Comics "Hell's Angel in Space" Lobo and is played with growly gutteral responses by Jemaine Clement from "Flight of the Conchords") who escapes from his maximum (and we mean maximum) security prison to find the man who sent him there 40 years ago—Agent K (Tommy Lee Jones). When he's unable to kill him here, the Boglodite finds another means to do so, and Agent J (Smith) wakes up the next morning, the only one with any memories of K past July, 1969. Agent K has been killed by Boris in the past, and J must journey back to try and save him.*
So, where does Men in Black III go from there?
Once back there, J negotiates his way through a 1960's era way of doing things. Everything's a little less high-tech (a little less), but the MIB Agency is still there, as is the much younger Agent K (Josh Brolin, doing a bang-on interpretation of Jones) and J must solve the puzzle of saving the Earth (of course), while keeping K safe. The past sequences are great—Men in Black has exploited the "fish-out-of-water" angle perpetually—and new corners are being thrown out the whole time (My favorite being a brief glimpse of a "Barbarella"-type being escorted around MIB, and although Smith is a bit too "Red Bull" throughout the entire movie, check out his understated reaction to some Black Panthers). 
Great cast, too. Rip Torn is gone, but David Rasche plays him in the past, Emma Thompson is on hand as the new MIB head, Will Arnett makes a brief appearance as does Bill Hader. Toss in the chameleon-like Michael Stuhlbarg as an alien able to read multiple time-lines and there's always someone to deflect the eye, or hand things off from Smith.
But, the best thing about this "Men-in-Black" installment is resonance. The other two were fine, the first better than the second just for its novelty, but had a shelf-life of three minutes. Part of it is Sonenfeld's way of comically undercutting any meaning to the thing, by changing perspective—"you think you got a handle on it yet? Well, let me throw THIS at you!" The whole "the Universe is so big and cosmic that there's no way you can understand it because there's so many mysteries, so nothing is real" concept, which is the backbone of the series (and the source for most of its humor) leaves one with a feeling of "meh"—nothing matters in a vast uncaring, unfathomable Universe.
* I'm not saying anything here that isn't revealed in the trailer.
