The Persian fleet landed at the Bay of Marathon, about 25 miles from the city of Athens. The Persians had a lot more soldiers, but they underestimated the fighting capability of the Greeks. The army of Athens routed the Persian army killing around 6,000 Persians and only losing 192 Greeks. After the battle, the Athenian army ran the 25 miles back to Athens in order to prevent the Persians from attacking the city. This is the origin of the Marathon running race.
The Greeks put together a small force, led by the Spartan King Leonidas I and 300 Spartans. They decided to meet the Persians at a narrow pass in the mountains called Thermopylae. The Greeks held off the Persians killing thousands, until the Persians found a way around the mountains and got behind the Greeks. King Leonidas told most of his troops to flee, but stayed behind with a small force including his 300 Spartans in order to allow the rest of the Greek army to escape