Morpheus makes his first appearance in the story "Out of Mind". Morpheus is responsible for giving the current Sandman, Sandman, his prophetic nightmares after coming into contact with him in a near death experience. Morpheus' first appearence in the story is when Dr. Dream begins terrorizing the Delightful Children in their dreams. When Sandman falls asleep, he calls out Morpheus to help free the operatives who fell victim to Dr. Dream, by ending their nightmares.
Morpheus originally worked with a man known as Novad York, bestowing him the Gem of Dreams in order to teach humanity responsibility. Morpheus sided with humanity in letting them rule the Earth, only to forever be condemned to his domain. After the death of Wesley Dodds, Nolan York inherited his prophetic dreams and his link to Morpheus.
After Nolan's apparent death, using the Gem of Dreams, Morpheus pulled Nolan's dying body into his domain. With Nolan on the verge of death, Morpheus sought out a successor as his envoy and connection to the physical world, eventually settling on Kayla Valera, Nolan's girlfriend and killer.
During KND: Galactic Endgame, Morpheus presents Kayla with a vision of Nolan, in reality Morpheus in disguise, in order to free her of her guilt for Nolan's death. Morpheus returns to his domain to find an angry, very much alive Nolan scolding him for his actions.
Morpheus argues that his actions were necessary and deems Nolan a failure. Morpheus toys with the idea of killing Nolan, but ultimately sides against it due to his connection to other successful envoys. He presents Nolan with an ultimatum, to go home and not interfere with his plans, or all of his friends would die in their sleep. Nolan sides with the former and leaves Dream's domain.
Morpheus would later appear before Nigel Uno, saving him from dying in space. Morpheus would then educate Nigel of his family's heritage and importance to the scales that Benedict Uno seeks.
The helmet Morpheus usually wears is made from the skull of one of his former foes.