The nuclear arms race was a competition in nuclear warfare between the United States, and the Soviet Union during the Cold War.
The first nuclear weapon was created by the United States, code named "The Manhattan Project" during World War II and was developed for use against the Axis powers.
The United States dropped the first nuclear bomb called the Atomic Bomb on August 6, 1945 on Hiroshimo, Japan at the end of WWII. Three days later we dropped a second A-Bomb on Nagasaki, Japan which resulted in 80,000 immediate deaths. The U.S. was the first ever in history to use nuclear weapons for offensive use. Later the Soviet Union came out with their version of the A-bomb during the cold war, but never used it on anyone.
The H-bomb was developed in the U.S. in 1951, during the cold war. The first test of this was the "Ivy Mike" nuclear test in 1952, conducted by the United States.
The nuclear arms race lasted from 1947-1991.