The area referred to here is roughly the portion of the larger historic region of Macedonia that is within Greek borders, and the largest of the major regions of modern Greece.
Philip II became king of Macedon in 359 BC, and defeated a army comprised of Thebans and Athenians in the Battle of Heronia in 338 BC; in the following year he used the promise of fighting the Persian to persuade the various city states (with the exception of Sparta) to unite under Macedonian rule.
Philip was assassinated, however, in 336 BC, by a Macedonian noble, and his throne fell to his twenty-year old son, Alexander, whose first tasks were squelching uprisings that followed upon his father’s death, demonstrating his power by totally destroying the city of Thebes when it rebelled against imperial Macedonian rule.
In 334 BC he marched his army of 40.000 into Asia Minor, and began taking possession of the Persian Empire, piece by piece, conquering Syria, Palestine, and Egypt, founding the city of Alexandria, and being proclaimed pharaoh of Egypt.
Next he defeated the Persian army of King Darius III, and pushed on into Uzbekistan (the territory now known by that name), Afghanistan, and northern India, believing that once he reached the sea beyond India, he would have conquered the world (given his concept of its limits).
His soldiers, however, had become exhausted from their long and arduous trek and in 324 BC, he was forced to turn back to Mesopotamia.
He became ill the following year, in Babylon, and died at the age of 33, leaving no heir. His generals carved up the empire he had won into three large kingdoms and some smaller states.
Ptolemy ruled Egypt, with its capital at Alexandria, founding the Ptolemaic dynasty, of which the last scion was Cleopatra, who committed suicide in 30 BC, thus end the genetic line. Selucus founded the dynasty named for him in Persia and Syria, with its capital at Antiokhia, and Antigonos ruled over Asia Minor, his successors later gaining control of Macedonia.
The Greek city states to the south were lost to Macedonian control and joined together in the Aetolian League, whose center was Delphi and the Achaean League, based in the Peloponnese. Sparta and Athens remained outside of these leagues.