Which two ancient civilizations fought in the Battle of Plataea?

The Battle of Plataea was the final land battle during the second Persian invasion of Greece. It took place in 479 BC near the city of Plataea in Boeotia, and was fought between an alliance of the Greek city-states (including Sparta, Athens, Corinth and Megara), and the Persian Empire of Xerxes I (allied with Boeotians, Thessalians, and Macedonians).

The previous year the Persian invasion force, led by the Persian king in person, had scored victories at the battles of Thermopylae and Artemisium and conquered Thessaly, Phocis, Boeotia, Euboea and Attica. In the summer of 479 BC the Greeks assembled a huge (by ancient standards) army and marched out of the Peloponnesus.

The Persians retreated to Boeotia and built a fortified camp near Plataea. The Greeks, however, refused to be drawn into the prime cavalry terrain around the Persian camp, resulting in a stalemate that lasted 11 days.

While attempting a retreat after their supply lines were disrupted, the Greek battle line fragmented. Thinking the Greeks in full retreat, Mardonius (the Persian ruler) ordered his forces to pursue them, but the Greeks (particularly the Spartans, Tegeans and Athenians) halted and gave battle, routing the lightly armed Persian infantry and killing Mardonius.

A large portion of the Persian army was trapped in its camp and slaughtered. The destruction of this army, and the remnants of the Persian navy allegedly on the same day at the Battle of Mycale, decisively ended the invasion.