Persians: The Persian Empire was the main adversary of the Greeks during the Greco-Persian Wars (492-449 BC). The wars began with the Persian invasion of Greece in 492 BC, and culminated in the Greek victory at the Battle of Plataea in 479 BC.
Carthaginians: The Carthaginians were a Phoenician civilization that controlled much of North Africa and parts of Spain and Sicily. They were the main rivals of the Greeks in the western Mediterranean during the 5th and 4th centuries BC. The Greeks and Carthaginians fought a series of wars, the most notable of which was the First Punic War (264-241 BC), which ended in a Carthaginian victory.
Romans: The Romans emerged as a major power in the Mediterranean during the 3rd century BC. They defeated the Greeks in a series of wars, including the Second Punic War (218-201 BC), and eventually conquered Greece in 146 BC.