Korean War
Korea, and most of west Asia were divided into sections, and each wanted each others territorty, and this ended up being a war. Russia was after non-communist china, while the Americans and the UN were defending South China.
Sputnik
Russia and the US were competing to see who can go to space first, as described as the space race. Russia managed to make it first, launching the first satellite, Sputnik, into space. This makes Russia slightly superior to the US.
Hydrogen Bomb is created/Arms Race
Russia and the US stockpiled weapons, and nuclear bombs during the Cold war. After the war was over, tensions decreased, and some weapons were disarmed.
Warsaw Pact
Was a collection of 8 communist/socialist countries to come together and form an alliance, similar to NATO. There also included a wall to separate East and West Berlin.
De-Stalinization
After Stalin dies, Isaac Deutscher came to power, and removed all of Stalin's Gulags and converterd Communist people into Socialist people.
U-2 Incident
An American scout plane was sent to Russia, and it was shot down. The Russians embarrased the Americans by saying that they were doing a test flight, and found numerous pictures of war bases and attack points.
Berlin Wall
A little after the Warsaw pact was assigned, Berlin split itself into East Berlin, and West Berlin to avoid starting a war.