Like the Middle Teton in the same range, Mount Moran's face is marked by a distinctive basalt intrusion known as the Black Dike.

No trails to Mount Moran have been maintained for over twenty years, and any approach overland requires a great deal of bushwhacking through vegetation, deadfalls, and bogs along the perimeter of Leigh Lake.

The first ascent of Mount Moran was made on July 22, 1922 by LeGrand Hardy, Bennet McNulty, and Ben C. Rich of the Chicago Mountaineering Club, via the Skillet Glacier route.

[5] The Direct South Buttress, a grade IV claim rated from 5.7 A3 to 5.9 C1, is a technical route suited for aid and Alpine climbing.

On November 21, 1950, a DC-3C cargo plane owned by the New Tribes Mission crashed on Mount Moran during a storm, killing all 21 on board.