There were two groups who fought in the Trojan War, and those were the Greek (also known as the Achaeans) and the Trojans.
Allegedly, prince Paris of Troy 'stole' Helen who was king of Sparta, Menelaus's wife. This sparked a war between the two groups, which lasted for 10 long years. According to the legend, even the gods were involved in the war, some taking the Trojan side, and some the Greek side.