I watched this with my son recently, last weekend. It told the story from a new perspective. An American family (with one child, a boy) living in Japan are split apart by an apparent accident at a nuclear plant. The parents both work at the plant but when what seems to be an Earthquake ruptures the reactor, the mother is locked in the exhaust tunnels and doomed to a radioactive death.
Years later the boy is a bomb disposal expert returning from a war zone. He is living in the US but is called to return to Japan to get his father out of jail. The nuclear plant is a restricted no-go area but the father keeps trying to get back in to find out what really happened. He has information about the wave form at the time.
It turns out that the wave form is electrical pulsing and a monster appears. Godzilla is a good guy and fights this new monster in the US. It's a good story and there is more to it than I can do justice here. It is a good film and I'd recommend it to fans of the monster movie genre.
There was a Godzilla film made in 1998. That one was poor compared to this one. The monster in the 2014 movie is a return to the original model of the Godzilla monster. The 1998 version made Godzilla look much too much like a T-Rex.