The Allied countries:
Great Britain, USA, China, Soviet Union', Poland, the Netherlands, Belgium, France, Czechoslovakia, Norway, Yugoslavia, Australia, Brazil, Canada, Greece, India, New Zealand, the Philippines, the Union of South Africa, many other countries.
The Axis countries:
Germany, Italy, Japan, Hungary, Romania, Bulgaria, Iraq, Thailand, other more or less aggressive countries
Major events in a nutshell Edit
On 1 September 1939 German's Wehrmacht invades Poland. Weeks later they have also attacked Holland, Belgium and France (over 10 individual countries).
By June 1940 the Allies have been pushed back and retreated over the channel. The Battle of Britain begins. On 22 June 1941 Germany invades the Soviet Union (Russia), moves far into the USSR but fails to take Moscow. The Siege of Stalingrad begins; Germany takes no more ground.
In June 1940 the Italians and Germans move across Libya and threaten Egypt. The Commonwealth respond and so commences the North African campaign. In December 1941 Japan attacks Pearl Harbour which drags the US into the war. Days later the whole world is brought in.
Japan soon attacks Malaysia, the Philippines and Burma, and so the Pacific and South-East Asia are also brought into the war. Japan soon takes over most of the Pacific and South-East Asia while Germany presses further across North Africa very close to Egypt. By Mid-1942 the Japanese and German advances are generally stopped. In late 1942 North Africa, the Allies are pushing the Germanys back across Libya, and by May 1943 Germany is out of Africa altogether.
In the same month, the Allies also start their campaign in Italy, which will push the Axis back up through Italy. By the end of 1943, the Allies were making some small gains against Japan in Asia and the Pacific. Their momentum started to pick up by mid-1944 as the Pacific was slowly retaken island by island; there was not as much luck in Asia. The USSR was taking some land back by the end of 1943 including Stalingrad, and in mid-1944 the The Red Army (USSR) strikes back. The Allies invade Western Europe in June 1944 with Operation Overlord.
The Allies initiated the failed offensive of Holland, they are not able to push the Germans back through into Germany. They slowly push the Wehrmacht out of Europe, but in December, Hitler orders the Ardennes offensive (in Belgium). This culminates in the Battle of the Bulge. A couple of months later the Allies have stopped the offensive and are pushing the Wehrmacht back into Germany.
The Wehrmacht are being rolled back to Poland and by 1945 the Red Army moves into Germany, and so do the British and Americans. Germany soon capitulates after Hitler commits suicide. Asia and nearly all of the pacific are retaken, while the Allies are on the Emperor's doorstep. Finally, the use of the atomic bomb on Hiroshima and Nagasaki, where Japan surrenders unconditionally… the second world war ends.
A more indepth article can be found here.