The BBC recently published an article entitled 'The fantastical beasts of ancient Greece', which is a wonderful read about ancient Hellenic art and the mythological monsters depicted in it, including Centaurs and Médousa. They also make a very good attempt in explaining the ancient Hellenic viewpoint on these monsters.

(Peter Horree / Alamy)    
The Metopes of the Parthenon depicts battle between Centaurs and men (Peter Horree / Alamy)

According to Peter Stewart, director of the Classical Art Research Centre at the University of Oxford:

"I don’t believe that Greeks really expected to meet a centaur or sphinx, or even a satyr, out in the countryside, and maybe they were always regarded as the stuff of legend. But a recurring trait of Greek art is that monstrous creatures seem to be held up as a foil to the Greeks’ concept of civilization – a sort of distorting mirror in which the Greeks could look at themselves. The Greeks seem to have found these monstrous or semi-human creatures useful to explore and express their world-view, their ideas about humanity and civilization, the mortal and divine. Fantastical beings were part of the furniture of the Greek mind."

Read more over at the BBC.