Incorporated in the 19th century by the colony of Victoria, the University of Melbourne is one of Australia's six sandstone universities and a member of the Group of Eight, Universitas 21, Washington University's McDonnell International Scholars Academy, and the Association of Pacific Rim Universities. Since 1872 various residential colleges have become affiliated with the university, offering accommodation for students and faculty, and academic, sporting and cultural programs. There are ten colleges located on the main campus and in nearby suburbs.

The university comprises ten separate academic units and is associated with numerous institutes and research centres, including the Walter and Eliza Hall Institute of Medical Research, Florey Institute of Neuroscience and Mental Health, the Melbourne Institute of Applied Economic and Social Research and the Grattan Institute. Amongst the university's fifteen graduate schools, the Melbourne Business School, the Melbourne Law School and the Melbourne Medical School are particularly well regarded.

Times Higher Education ranked the University of Melbourne first in Australia and 31st globally in 2021, while the Academic Ranking of World Universities places it 35th in the world (both first in Australia and the whole of Oceania). In the QS World University Rankings 2021, the university ranks 41st globally and 3rd in Australia. Four Australian prime ministers and five governors-general have graduated from the University of Melbourne. Eight Nobel Laureates have taught, studied and researched at the University of Melbourne, the most of any Australian university.

The university's coat of arms is a blue shield on which a depiction of “Victory" in white colour holds her laurel wreath over the stars of the Southern Cross. The motto, Postera crescam laude (“Later I shall grow by praise" or, more freely, “We shall grow in the esteem of future generations"), is written on a scroll beneath the shield. The Latin is from a line in Horace's Odes: ego postera crescam laude recens.