Prior to the creation of humans and Amazons, all of the Olympians would dwell on and oversee Earth from Mount Olympus, hence they would be forever after also known as the Olympians. The king of the Olympians, Zeus would justly rule over his siblings and children.
After Zeus' creation of Mankind and later the Amazons, Zeus' malevolent son Ares would rebel against all other gods in a jealous rage, and instigate the devastating War of the Gods, which took place on Olympus.
Growing more powerful from the violence of the war he instigated, Ares fought and slew the other gods as they attempted to bring him down until only Zeus was left as he did not participate in the war at first and instead fathered Diana (as a contingency dubbed the 'Godkiller' that could one day defeat Ares) with Hippolyta as a contingency plan should he fall to Ares. Zeus then fearlessly confronted the dramatically enhanced and malevolent God of War and eventually defeated and grievously injured him, banishing him from Olympus and greatly weakening him even centuries later. With the last of his powers, Zeus created the magical island paradise Themyscira for the Amazons to live, hidden from the God of War. Following the war, Olympus would be left empty, with the banished Ares seemingly unable to return.
Mount Olympus is portrayed as an immense mountaintop from which the gods gathered, surrounded by numerous clouds, that overlooked the Earthly plane. From their vantage point, the gods could easily affect mankind, with Ares notably being depicted as imbuing humans with violent impulses from his perch on the mountaintop.
It is unknown if, as in mythology, there were architecture build on Mount Olympus by the gods.