Their punitive expedition against Eretreia and Athens losing the battle of Marathon to the Athenian and Plataean armies.
The Athenian and Plataean armies defeat of the Persian expeditionary force convinced other Greek city-states that they could hold off Persian attempts to dominate them.
There were dozens, large and small. The most decisive were: 480 BCE Artemesium - Greek defeat 480 BCE Salamis - Persian defeat 479 BCE Plataea and Mycale - Persian defeats 466 BCE Eurymedon - Persian defeat 450 BCE Cyprus - Persian defeat
Persian empire
Marathon
The Battle of Marathon was the first attempt , and first defeat , by Persian forces to subjugate Greece . The Persians were defeated by the Athenians at Marathon , Greece .
They didn't defeat a war. They defeated the Persians in the Persian War in the eastern Mediterranean on land and sea 499-449 BCE.
By the Greek city-states combining to defeat the Persian army and navy.
Darius was a Persian.
Persian Empire
The Persian Empire.
Being outmanoeuvred by Alexander the Great - who first slaughtered Greeks who were bolstering up the Persian army, then putting an end to the Persian fleet by occupying their bases in the Mediterranean, then capturing the Persian treasury which enabled him to pay his army, and inflicting a final land defeat of the Persian army.
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.