The space race was a competition between the Soviet Union and the US to achieve firsts in spaceflight capability.  It had its origins in the ballistic missile-based nuclear arms race between the two nations that occurred following World War II. This competition began in earnest on August 2, 1955, when the Soviet Union responded to the US announcement of intent to launch artificial satellites for the International Geophysical Year, by declaring they would also launch a satellite “in the near future”. 

Two years later the Soviet Union achieved the first successful launch with Sputnik 1, October 4, 1957. This was the first object in history to fly around the earth. This came to a big surprise for the US and the rest of the world, which resulted in the Sputnik shock. The Soviet Union wanted to show the world how powerful and big their rackets were, and how they also could be equipped with nuclear weapons. 

The US entered the competition to be the first human in space. But the Soviet Union sent the first human to space, April 12, 1961. His name was Jurij Gargarin. 

  Almost a month later Alan Shepard was the first American in space, May 5, 1961 with “Freedom 7”. When the plans for the third manned space program, Apollo, was presented May 25, 1961, President John F. Kennedy said in front of Congress that the US should have a goal to have the first human on the Moon before the decade was over. The first launch of an Apollo spacecraft took place in 1967, and the first Moon landing in history was completed July 20, 1969. Neil Armstrong and Buzz Aldrin with Apollo 11 were the first humans to set their feet on the moon.

Valentina Tereshkova from the Soviet Union was the first woman in space with Vostok 6, June 16, 1963. Several missions were planned with Vostok, but when the Americans announced the Apollo-program, Nikita Khrusjtsjov (a politician) demanded that the Soviet Union should have more than one passenger in space. This led to Voskhod 1, a modified Vostok vessel, that carried Vladmir Komarov, Konstantin Feoktistov and Boris Yegorov to space October 12, 1964.

Aleksei Leonov also from the Soviet Union was the human on a spacewalk with the Voskhod 2-expedition mars 18, 1965. The mission could have gone terribly wrong. Aleksei was barely able to return to the spaceship. During the trip back to earth, the rockets didn’t work optimally, which caused Voskhod 2 to miss their planned landing area with 1600 kilometers. 

Earlier these two nations have sent animals to space. Technically, banana flies, launched on V-2 rockets in 1946 by the Americans, the first animals in space. The flies were used in scientific studies, and the first mammal in orbit around the earth, the dog Laika, flew in Sputnik 2 in 1957. The dog Laika was sent up by the Soviet Union. The technology of the time couldn’t save Laika, the dog died shortly after it reached the space, of stress and hyperthermia. In 1960 the Soviet Union sent the dogs Belka and Strelka in orbit around the earth with success. The American space program sent at least two chimpanzees to space before using humans. In September 1968, the Soviet Union sent turtles on the expedition Zond 5, which sent the first animals to fly around the moon. Later, more animals have been used in space-related research, but resistance in the population ended this in the latter part of the 1990s.

Sputnik was the start of the Space Race, but it's a bit more contentious when it ended. Most of the competition took place in the 1960s, which resulted in the moon landing in 1969. The Americans claimed that they have won the race after they reached the moon. The Soviet scientist continued their work without caring about the landing. The Space Race became calmer after the moon landing. Some people characterize this the end on the race, but most historians consider the end to be the link between American Apollo and Soviet Sojuz 19 in 1975.

The Soviet Union was the best on rockets at the end of the Cold War, and the US was the best in RC and electronics.