The Macedonians from Northern Greece, led by Philip II and his son, Alexander, conquered nearly all of Greece. Then Philip died and Alexander III became king in 336 BCE.
A popular story about Alexander is that one day, his father, Philip the Great, wanted a new horse. He saw one horse that would do well in battle, but was too wild to ride. Alexander wanted to ride it. Philip was surprised and said that Alexander could have the horse if he was able to ride it. Alexander saw that the horse, Bucephalus, was afraid of its shadow. Philip bought it and Alexander used Bucephalus in every battle that he fought.
Alexander III, also known as Alexander the Great, had even greater goals in mind: to take over Persia. Persia was the largest empire in the world at the time. But that didn't stop Alexander.
He gave Greece to one of his generals, Antipater ( who would later conquer Sparta). Then he set off for Persia.
The Persians, led by their king Darius III, went to meet him at Issus, 333 BCE (see map). The Persian army contained 300,000 men as opposed to Alexander's 40,000.
But that didn't stop Alexander. He defeated them and marched on towards Egypt (332 BCE).
He met the Persians at Gaugamela, 331 BCE, and defeated them again. Darius III himself fled, with Alexander in pursuit.
Finally, one of Darius' generals, Bessus, killed Darius and declared himself Artaxerxes V, King of Iran.
But since Alexander wanted to be the one to kill Darius, he got so angry he killed Bessus (Artaxerxes V) and took over the rest of Persia (now called Iran).
He then continued on to Pakistan and North-West India. He conquered the Indian king Porus' kingdom (326 BCE).
The Macedonian Empire at Alexander's death.
Alexander wanted to go further, but his army refused, because of the looming threat of the Nanda Empire, a predecessor to the Maurya Empire. So he turned back home to his capital, Babylon (325 - 324 BCE), attempting an invasion into Arabia, but he died in June, 323 BCE.
However, this was not the end of the conflict! Many generals claimed control of Alexander's former empire. At first, the General Perdiccas tried to conquer Ptolemaic Egypt, but failed and was killed. Next another general, Eumenes, battled against Antigonus. At first, Eumenes was winning, but then the baggage train, with the prestige soldiers' relations and most prized possessions, was taken, likely by Antigonus himself. They took Eumenes to Antigonus, where he was starved for three days, and then killed. Antigonus and his son Demetrius now launched many campaigns against other generals, successfully defeating them. But everything changed in 301 BCE, when the armies of numerous generals went against him. Antigonus remained on the battlefield, never losing hope in his son. He died there, aged 81, and Demetrius, very competent, conquered Macedon, though Rome took it over many years later, under one of Demetrius' successors.