Ancient/Classical history focuses mainly on the Indo-European language-speaking Romans and the Greeks. The Greeks lived in the area on the southern part of the Balkan peninsula (generally, but not categorically, south of Epirus and Thessaly), in the Peloponnese, in islands around the Aegean Sea, along the coast of Asia Minor where many Ionian Greeks lived, and in a region known as Magna Graecia in the southern area of Italy, and in Italy's islands.
The Greeks are generally counted as the descendants of Hellen, but in the Homeric version of the Trojan War, the poet refers to them by the names of their individual cities or as Argives, Danaans, or Achaeans. Earlier Greek people were the Mycenaeans.
We get the term Greek from the Romans. The term Graecia is the Latin for Greek, but the Greeks called themselves Hellenes; their country even today, Hellas.
Eventually, the Roman Empire spread eastward, setting up a new capital city in an area then part of Greece, now part of Turkey, at Constantinople. For the next few centuries, this Greek center grew in importance, while the city of Rome diminished. By the late period of the Roman/Byzantine Empire, the Greek-speaking people might be referred to as either Romans or Greeks. As Christianity took over as the official state religion, "Greeks" might refer not to any racial or linguistic origin, but simply to pagans.