Ashur is the odd one out in the Mesopotamian pantheon, and the oddity is theological rather than trivial.
Most Mesopotamian gods have a domain and a personality: Enlil holds authority, Inanna holds sex and war, Nanna is the moon. Ashur has almost no mythology of his own. He is not the subject of stories, he does not appear in the great narrative texts in a developed role, and he has no clearly defined natural sphere. What he has is a place. The same name, Ashur, denotes the god, the city, and eventually the empire, and the three are not really separable. He is best understood as the deified city itself.
This produced a distinctive theory of kingship. Assyrian kings did not claim divinity. They styled themselves the steward or vice-regent of Ashur, holding the land on the god's behalf and accountable for it, and their inscriptions are framed as reports back. That is a markedly different arrangement from Egypt, where the king was a god, and it gave the Assyrian state a permanent justification for expansion: enlarging the territory was enlarging the god's estate, which was the steward's job.
The city kept its ritual primacy after losing its political one. When the court moved to Nimrud and then Nineveh, kings still came back to Ashur to be buried and to conduct the akitu New Year rites, for which a dedicated building stood outside the walls.
Walter Andrae excavated for the German Orient Society from 1903 to 1914, and the work was unusually careful for its date: he traced mudbrick stratigraphy, which earlier excavators had routinely dug straight through without registering, because unfired mudbrick against mudbrick is nearly invisible unless you are looking for it. The finds went to Berlin.
The site was inscribed on the World Heritage list and placed on the List of World Heritage in Danger in the same year, 2003, the stated threat being a proposed Tigris dam whose reservoir would reach it. The project has been revived and shelved repeatedly and has never been formally abandoned.