The underworld in Greek mythology is a vast and shadowy realm, separate from the world of the living and the realm of the gods on Mount Olympus. It is described as a dark and somber place, where the shades or spirits of the deceased reside after they have crossed over from the land of the living.
Hades' dominion extends over the entire underworld and its inhabitants. He is often portrayed as a stern and unforgiving figure, ensuring that the dead remain within his realm and are subjected to their respective punishments or rewards based on their actions during life.
While Hades is primarily associated with the underworld, he also plays a role in the affairs of the gods and mortals on Earth. In some myths, he is depicted as joining his brothers Zeus and Poseidon in various events and interactions with humans and heroes.
Overall, Hades resides in the underworld, where he rules over the realm of the dead and maintains the balance between the worlds of the living and the dead in Greek mythology.