The reason why they were fighting was that the Persians took their farmland and harbors. They forced the Ionians to pay tribute and serve in the army.
Battle of Salamis
During Marathon 490 B.C.E the persians got mad at Athens for them helping the Ionians. The Athenians won the war because of their phalanx formation strategy. The runner up Pheidippidies ran about 26 miles to warn Athens of the Persian army coming.
Battle of Plataea
In 480 B.C.E (during Thermopylae) Xerxes took over when King Leonidas his father died, then he leads his soldiers into Leonidas. They tried to hold off the Persians but all 300 men died. They died because the Spartans controlled the narrow pass through which the Persians had to pass.
Effects of war
During Salamis 480 B.C.E the Athenians tricked Persia to fight in a narrow channel where the Persian ships could not turn around to retreat, Persian ships were much bigger than Athenian boats were. The reason why the Athenians sailed nearby the islands was because they heard about the Spartans defeat in Thermopylae and knew the Persians would soon destroy Athens.
When the Battle of Plataea 479 B.C.E The Greeks had defeated the Persian army that Xerxes had left behind. The Persian wars were important because they preserved Greek independence and prevented Persia from conquering all of Europe.
Athens was the Greek city-state to establish the Delian League which helped them in the war. Xerxes left his army behind to retreat. Then finally the Greeks won the war.