Being the master of dreams, Morpheus had the ability to send images to the visions of people, to shape these images and give a form to the creatures that lived in dreams. Morpheus himself had a talent in mimicking any human in the dreams, and was able to take any form he wanted.
When in his real form Morpheus had wings on his back. It was believed that he and his brothers were given wings by their uncle Thanatos, the deity of death, although some interpretations said that they were wing-born.The legend says that Morpheus used his wings not only to reach those who needed help in their dreams but also to carry his father, the wingless Hypnos, to the dream world in the caves, when in several occasions needed to be saved from Zeus' menace.This version also suggests that Hypnos was a pretty lazy deity, spending most of his time sleeping.
The Dream World of Morpheus was the place where his family lived. While shaping dreams of mortals as he wished, and visited countless bedrooms, Morpheus slept in a cave full of poppy seeds. That mythical fact is maybe why morphine (known as morphium as well) – opium based medication for severe pain - borrowed its name from Morpheus.
The River of Forgetfulness and the River of Oblivion were found in that world, highly protected by the gates under the supervision of two monsters that would easily materialize the fears of any uninvited visitors. The legend says that only the gods from Olympus were allowed in this family nest.
Morpheus didn't have a wife, or at least so it was known in the Greek mythology. But some interpretations were ready to see him with Iris, the personification of the rainbow and messenger of the gods.