The Ionian Greeks had a revolution against Persian. Athens sent soldier to help them and because of this, Persia was MAD
When the Persians landed in Greece, the Athenian army attacked them while they were getting off of their ships, they were successful;, and had a runner named Pheidippides to tell Athens of the victory
At Thermopylae, 300 Spartans held off the Persian army long enough for Athens to evacuate. Unfortunately, all 300 Spartans were killed by the Persians.
The battle of Salamis was a naval battle, where the Athenian Navy led the Persians into a narrow channel. The Persian's larger ships had a harder time moving around, so the Athenians had the advantage. Most of the Persian navy was destroyed in that battle.
The battle of Plataea was the final battle of the Persian wars. The Athenians fought bravely, and drove the Persians out of Greece!
After the wars, and alliance between Athens and the surrounding city states was formed, called the Delian League. Things were not so great for Sparta, they had become very poor, and went through some tension with Athens