479 BCE at Plataia.
It was the Battle of Thermopylae in the Second Persian War. The Greeks won. Shortly after Thermopylae the Athenian Navy defeated the Persian Navy at Salamis, and in the next year the Persian Army was defeated by a combined Greek Army at Plataea.
480 BC .
The Persian War 499-449 BCE ended with a settlement where the Persians agreed with the anti-Persian Delian League to stay away from Greek city-states in the eastern Mediterranean littoral. The Persians had revenge when they helped the Peloponnesian League led by Sparta to defeat the empire Athens had turned the Delian League into. The Greek inter-city wars continued on unabated, and Persia re-established control over the Asian-Greek cities again as the mainland Greek cities were too busy fighting amongst themselves to worry about them.
After destroying Persian sea power at the battle of Salamis, they were able to defeat their army, and so end the attempt by the Persians to incorporate the cities of mainland Greece into the Persian Empire.
The sea battle of Salamis defeated the Persian fleet which had to withdraw back to Asia Minor, leaving the Persian army unsupported and without its supply fleet, so half of the army had to go home. This left the reduced Persian army open to defeat at Plataia the following year and the invasion was defeated.
in 1813, napoleon was defeated in the Battle of the Nations at Leipzig.IMPROVEMENTNapoleon's army was defeated in Russia in the year 1812.
The Spartans did not 'follow' the Persians - they were part of a blocking force which delayed the Persian army for three days, and had no effect on the following two-year campaign which defeated the Persians at the battles of Salamis, Plataia and Mycale.
Persia had invaded mainland Greece. A coakition of Greek city-stated defeated the Persian navy in 480 BCE. The following year they assembled their armies at Plataia to defeat the Persian army and so finish off the Persian invasion.
Persia invaded Greece. The southern Greeks decided that if they could defeat the Persian fleet, the invasion would be exposed to defeat on land and could not be fed in such a poor country in winter. The defeat of the Persian navy at Salamis resulted in the withdrawal of half the Persian army and its subsequent defeat the following year when the Greeks assembled at Platia.
Some were sunk, some captured, some retreated, and some were victorious. The Persian remnant was withdrawn to Mykale in Asia Minor, where they were captured the following year by the Greek fleet at the same time as the Persian army was defeated at Plataia. This ended the Persian invasion.
Marathon was a plain, not a city. It was owned by Athens. They fought a battle against a Persian amphibious punitive expedition sent by Persia in 490 BCE.
450 BCE Cyprus.