What were the main features of the nuclear arms race

SPACE RACE - Spunick (not sure if I spelt that right - the USSR space craft) was launched which caused the United States to invest more money into mathematics and sciences to grow and gain scientist to work at NASA.

We also started building tons of atomic bombs because we found out that there were spies at los alamos where bombs were being built. the USSR used to be on good terms with the usa because they were an enemy of our enemy which caused us to like each other but after hitler was gone we were enemies because we didn't want the same thing to happen with communism like what hitler did (taking over Europe)