There was a fantastic TV series by the same name in 1988 that actually served as a sequel to the movie as well as tying in the radio broadcast in the same world. 1938 was explained as a "test run" that the government used to test our reactions to a potential invasion. 1953(the movie) was the actual invasion, and though the movie portrayed that the aliens died at the end, the tv series posited that they only went into hibernation, and the us government gathered up the bodies and machinery and tech and sealed it all away, Raiders of the Lost Ark style. Then they awoke.
Highly recommend it. The first season, specifically. The second season should only be watched if you have weed handy.