A Valyrian sphinx is a mythical creature, with the body of an animal (most likely a dragon) and the face of a human. The Valyrians made statues of Valyrian sphinxes, some very large, and often in male-female pairs. Valyrian sphinxes are now relics, left over from Old Valyria, prior to the Doom. They are still seen in parts of Essos, though some have been moved as far afield as Vaes Dothrak, the Iron Islands, and the Red Keep in King's Landing.
A Game of Thrones
A Clash of Kings
As Tyrion Lannister enters the Red Keep’s council chamber, he pauses to admire the Valyrian sphinxes at its entrance, and rests his hand on the head of one of them just before he leaves, indicating that they are not the same scale as some of the vast Valyrian sphinx statues.
A Feast for Crows
A Dance with Dragons
While travelling, Tyrion Lannister and Illyrio Mopatis come across a huge Valyrian sphinx crouched beside the road. It has a dragon's body and a woman's face. However her king is missing, dragged off by the Dothraki back to Vaes Dothrak on wooden wheels. Why the Dothraki did not take the queen sphinx is not mentioned. There is a smooth stone plinth where the king once stood, grown over with moss and flowering vines. Tyrion Lannister considers the "dragon queen" sphinx a pleasant omen and her missing king being dragged back to Vaes Dothrak an omen too, but not as hopeful.
The Long Bridge, which joins the two halves of Volantis across the mouth of the Rhoyne, has a Valyrian carved gateway that is an arch of black stone carved with sphinxes, manticores, dragons and other strange beasts. It is not stated whether the Valyrian carvings are of lion bodied sphinxes or Valyrian dragon sphinxes.