Cyrus' son, Cambyses II, inherited the Persian throne in 529 BC. In 525 BC he invaded Egypt and conquered Pharaoh Psamtek III. He soon died, however, on his way back to stop a revolt breaking out in Persia.
Darius, a general in his army, continued homeward to crush the rebels, after which he usurped the throne. Under Darius I (522-486 BC) and Xerxes I (486-466 BC) the Achaemenid Empire reached its greatest extent. Darius also had to suppress revolts, in Ionia and Egypt.
He extended Persia's eastern frontier into northern India and his northern frontier into Europe. He attacked the Scythians north of the Black Sea, conquered Thrace and Macedonia, but when he attempted to subdue Greece, he met with defeat at the battle of Marathon in 490 BC.
Xerxes succeeded his father in 486 BC and had quickly to deal with rebellion in Egypt and Babylon. He was less tolerant of other religions than his predecessors had been and he suppressed the 'false gods' of those two rebellious nations.
In 480 BC he launched the long awaited invasion of Greece. After initial victories, his forces were defeated and repelled. Xerxes then lost interest in further Persian expansion. He lived a decadent life in his royal palace at Persepolis, until a conspiracy organized in his harem led to his assassination in 465 BC.