Mythology is a collection of tales about gods and heroes. The Greek nation, divided into many tribes, wasn't sharing a one common story about its deities. Every small state (polis), every village or community had its own version that was freely transformed and changed by poets. In that way a rich and diverse collection accumulated during all these ages.
The Greek Pantheon represents a very complex combination. There are numerous myths, created by many societies and scattered throughout big area and long time. Before they were put in order, myths had represented different, sometimes even contradictory, versions of the events. Some of them came from the East, like the Asian myth about the golden, silver and iron ages. Local superstitions and beliefs in myths were the cradle of the Greek religious experience. Greek gods and goddesses remain humane, although they are supernatural. Their character is a forecast of later anthropocentric nature of the Greek civilization.
Despite many Eastern or Egyptian borrowings, the Greek mythology shows gods as people - better or worse, but humane. Whatever was it caused by, it was a real revolution - its complement was the faith that it was possible for people to become like gods. Tendency to show gods as people is very clear in works of Homer, who shaped the Greek conception of Olympic gods more than anybody else. Homer's gods interfere in the Trojan War and compete with each other. Homer attributed gods everything that was shameful and reprehensible in people's nature: theft, adultery and lie. Gods' world was very similar to human world.
Demigods, whose lives were described in legends, played an important role in the Greek mythology. Outstanding people who deserved gratitude, became, after their death, demigods. So demigods were mainly founders of dynasties, lawmakers, war heroes, priests, prophets, great poets, and people who improved people's life with their inventions. A demigod's grave was a great sanctity of the community. It was usually located on a market square, at a gate or on a community's border. Sometimes the grave was a mystery, in fear of the enemies, who could steal the holy relics. Over the grave a chapel (heroon) was built, surrounded by an olive or cypress grove. No single branch could be taken from these groves, under a severe penalty. At the grave there was a small altar, with a ditch around, to collect the offerings' blood. The church service took place at night or at dusk.
In the moments of terror people raised their prayers to demigods because these guardians could come to their rescue most easily. Many demigods were depicted as snakes. A snake, crawling on the ground, hiding in a cleft was to indicate underground nature of these demigods. On demigod's graves temples were erected and Olympic Games took place.
So demigods were a part of Greek beliefs. In many cases they were treated equally with gods, they were acknowledged as half-gods or sons of the Greek gods.
Everyone who goes into the vivid world of myths and legends can not help asking a question: how did mind of such an intelligent nation manage among these contradictions, sulks and heinousness?
The history of the Greek religion answers that question. It contains thousands of years of fight between common sense and virtue, superstition and unrestricted imagination. The definition of divinity was cleared of superstitions and immoral myths and legends in mystery plays, priest colleges (e.g. the Delphi College), by philosophers (Plato) and poets connected with religion (Aeschylus, Sophocles, Pindar). The definitions were changing from century to century but unexpectedly the end of the Ancient Age was very similar to its remote beginnings. Even extraordinary minds were overcome by belief in demons and there were lots of miracle-workers, magi and witch doctors among the philosophers, which Homer despised.
All that has been examined by historians for a hundred years only, no-one was interested in it for fifteen centuries, when the world of Greek gods had the biggest influence on the European literature and art. Mythology was always perceived as one of the most beautiful creations of Greek imagination. It was a collection of immortal subjects, motives and symbols without which art couldn't exist its way today and to which it still gets back.