The Athenians did not fight at Thermopylai. A combined force of half a dozen other cities did. The Athenians manned their fleet at the parallel sea battle at Artemesion which was lost.
Athens evacuated its populace to Peloponnesian cities and embarked its forces on its warships to fight in the Southern Greek fleet at the successful battle of Salamis, after which they returned to Athens which the Persians had evacuated.
The Persians defeated the Greek, with each side losing a few thousand casualties.
The Athenians were not part of the force at Thermopylai. They were manning their navy, which was part of the naval force assembled at Artemesion in the nearby strait fighting the Persian fleet. After the sea battle was lost, the fleet retired to Salamis for another try. Meanwhile, they abandoned their city, sending their non-combatants to refuge in Peloponnesian cities.
The Greek fleet lost the naval battle of Artemesion to the Persians. As the defence of the Thermopylai pass had been to force the naval battle, the force holding the pass was withdrawn as having no further purpost. A second successful sea battle was fought at Salamis.
In fact they crushed the Greek delaying force at Thermopylae an also defeated the Greek navis in the nearby Strait of Artemesion. After both these victories, they moved into southern Greece and occupied Athens.
The Persians defeated the Greek, with each side losing a few thousand casualties.
Their punitive expedition against Eretreia and Athens losing the battle of Marathon to the Athenian and Plataean armies.
First, by a stratagem they were able to convince the Persian commander that the Greek fleet would try to flee through the back entrance to the Strait of Salamis, so the Persians diverted the 200-ship Egyptian contingent to cover that escape route. This evened up the fleets for the main battle. Second, by positioning themselves inside the Island of Psytallia, this required the Persian fleet to split in two, and each to enter the strait on a narrow front, so that the Greek fleet was able to attack the Persian columns from the flanks. This, and the closeness of the shores minimised the manoeuvre space for the nominally larger and superior Persian triremes. The Persians were not helped by the fact that they had been sitting at their oars outside the Strait all night to stop an expected Greek breakout, and were tired before they got into the battle the following morning, and a strong wind had raised the waves and pushed against their higher ship sides, making manoeuvre more difficult for them. The Greeks had tried this at Artemesion opposite Thermopylae and come off second best. This time they picked the right location and overwhelmed the opposition.
The Battle of Yorktown
a losing battle
At the Battle of Marathon, the Persians and Athenians fought. The Persians outnumbered them, but Athens still won.The Athenian and Plataian infantry remained in the hills around the Plain of Marathon where they were safe from the Persian cavalry. They were awaiting the reinforcement of the Spartan army.The observed the Persian cavalry being embarked, and took the opportunity to run down and defeat the inferior Persian infantry unprotected by its cavalry, and routed them.They then realised the Persian cavalry was being shipped around Cape Sounion to land near Athens and gallop up and take the undefended city as the gates were opened by traitors within. They ran back the 26 miles to the city and formed up in front of the gates just in time. The Persians gave up and went home.The Athenians made this run in sandals, carrying armour and weapons, after having already fought the battle at Marathon.Today's marathon runners who think they replicate this run get it pretty easy by comparison.
Rome.
Bloody..