The Soviets and Cubans invade the United States, and a small band fight to survive.
It's important to understand this movie in the context of the Cold War. As such, this movie doesn't exactly stand the test of time in this respect. The 2012 remake had to blame North Korea because our times are different. Back then, this movie had a believable-enough plot line.
The underlying ideas are good, but the actual plot and movie itself do feel old. I like this movie a lot, but only for its concepts. I don't think it's re-watchable for a non-survivalist.
This was remade as Red Dawn (2012 film). That version sucked.