I really want to add some positive comments about this film to balance the negative reviews concerned about what the film didn't have in it, and the feelings of disappointment simply because the director wanted to take a different stance on an alien 'invasion'.
Apparently the director and actors had no script to work from, a very small production team, and a minute budget, which makes the finished result quite an achievement. Just like the `Blair Witch Project' was.
This is my understanding about why the 'creatures' are rarely seen by the people in it, and the audience.
Basically from what I can glean is that the creatures spend the majority of their time living in water and emerge once a year to spawn their eggs in the surrounding forest plants (possibly after finding a mate) before returning to the water. They seem to be portrayed as quite gentle creatures that rightly so attack any humans who try to destroy them, their young, or their habitat, just like any other intelligent creature on Earth would too. Their calling sounds and immense size reminded me of elephants or whales (both very large and frightening, but capable of being gentle). Also, if you were one of the creatures and every time you were spotted you were attacked, you would try to stay as hidden as possible too.
Some points in the film were a little confusing but I think that is because the army seemed to be keeping a lot of information from the civilians and maybe even giving misinformation. I first assumed that the people needed gas masks because the aliens were producing toxic gas as a defense, but it seems that this gas was being dropped by the army to kill the alien eggs in the plants.
Why was there a massive opening in the defense wall that people could just walk through, who knows? Something seemed to have been happening in the area on the American side of the wall that gave the impression that the army had been forced to abandon it.
For me there were definitely moments of building tension while I was watching the film and this was because we never fully saw the whole creature until the end. The misfiring boat engine almost gave me a heart attack... It was all very reminiscent of the tension of a river and jungle trip from a Vietnam war film.
By far the most frightening part of the film is the realization that there is seemingly absolutely nothing the Americans can do to eradicate the alien spawn and the best hope is to try to live with them, which seemed unlikely. For me, the director managed to make this simple scenario a very believable possible future for the Earth.
I won't argue that this is a slow paced film. It's slow paced like the film 'The Road', which is another end of the world scenario where events are explained far less than in `Monsters'. If you like end of the world survival films (I love them) and you liked `Monsters' do check out `The Road' but be warned it's much more brutal and disturbing, doesn't involve aliens, but does portray the best and worst sides of human nature much like `Monsters'.