At the start of the war, the Persians grew tired of waiting after 3 days for the Greeks. That's when they attacked! Persians were out of formation. The Greeks won the battle of Marathon.
After their defeat, the Persians wanted revenge. In Themosticles, the Persians attempted to cut off the Greek supplies. After a traitor told them a Greek route, the Persians attacked from behind. King Leonidas knew they'd be surrounded. He and 300 troops fought to the death.
After the Spartans defeat, the Athenians made a plan to lure the Persian ships into a narrow strait. Persian ships were too large and could not navigate like the Athenian ships. They suffered many losses.
After another humiliating defeat, the remaining Persian soldiers went to Athens. Finding it nearly completely empty, they set it on fire.
In this final battle, all of the Greek city-states came into alliance. The Persians were now evenly matched. The Greeks ultimately beat Persia in the battle of Platea
After the Greeks gained their independence, the Persian empire weakened. The people grew unhappy due to unreasonable taxes. The empire was no longer able to defend itself. It was taken over by Alexander the Great.