Before I get into what Monsters is about, just watch the pretty good trailer.
So the plot of Monsters starts out that NASA thinks their alien life in our solar system. so they sent a probe to collect samples everything going good until said probe re-enters earth and breaks up in the atmosphere over Mexico. The small ailen microbes thrive on earth and transform into massive ailens. The US builds a huge wall/fence to keep these creatures out of the US and the uncontaminated side of mexico does the same.
So there's the back story against which the whole movie is set. The human element of the story comes across by a photo journalist tasked with getting pictures and documenting the destruction caused by the alien's lifeforms and/or armies. However, his bosses daughter is in mexico and was caught in some attack or other natural disaster. So of course his job is to now get his bosses daughter back home to America where it's safe.
I won't explain anymore then that. I thought the movie was okay, but the trailer made it seem like it was going to be a really good movie. I am glad I watched it once but only because I had "nothing" else to do/watch.
I would say its 1 part Lost in Translation, 1 part District 9 and 1 part Cloverfield. However, since I saw all 3 of those movies (all at the movies oddly.)
This movie just didn't grasp me the way it could have done.