Key events (hugely simplified):
1933 Adolf Hitler takes power in Germany, with a policy of gaining "lebensraum" (living space for Germans).
1937-1938 Hitler declares that various states are full of oppressed Germans, and takes them over with little recourse from Western powers. (note the similarity to Putin)
1939 Germany invades Poland and WW2 begins. Both Russia and Germany take over Eastern Europe.
1941 After having agreed with Stalin to share the spoils in Eastern Europe, Hitler turns on Russia and nearly defeats them, getting to within miles of Moscow.
1944-1945 Fortunes have now turned and Russia slowly makes its way through Eastern Europe, taking over in these countries. The Allies agree to split both Berlin and Germany. Allied areas are free to embrace democracy, whilst Russian areas were run by Communists in deference to Moscow.
1949 NATO is formed to protect Western European Countries against further Soviet aggression. It is an agreement that if any country is attacked, all members must defend that nation. This is part of the cold war.
1988-1991 The USSR collapses, and all the countries occupied by the USSR in 1945 gain independence. Ukraine also gains independence, and agrees to give up Nuclear weapons if Russia promises to respect its sovereignty.
1991 onward: Former Soviet countries look increasingly to the West, joining both NATO and/or the EU and embracing democracy. Russia becomes an oligarchy, eventually to be led by Putin. Putin slowly takes on the role of dictator, destroying democracy. Putin want to regain some of the "glory" of the USSR, looking to retake places like Georgia and Ukraine.
2014 Russia invades Crimea, part of Ukraine and takes it over.
In Ukraine there are still some areas that are somewhat Russian speaking, and have independence movements, backed by Russian money. Putin last night declared these regions as independent, and has moved in troops to guarantee their independence, in effect annexing them.