Edinburgh receives over 60,000 undergraduate applications per year, making it the second-most popular university in the UK by volume of applications. It is the eighth-largest university in the UK by enrolment, with 35,375 students in 2019/20.Edinburgh had the seventh-highest average UCAS points amongst British universities for new entrants in 2019.The university continues to have links to the British royal family, having had Prince Philip, Duke of Edinburgh as its chancellor from 1953 to 2010 and Anne, Princess Royal since March 2011.

The alumni of the university include some of the major figures of modern history. Inventor Alexander Graham Bell, naturalist Charles Darwin, philosopher David Hume, and physicist James Clerk Maxwell studied at Edinburgh, as did writers such as Sir J. M. Barrie, Sir Arthur Conan Doyle, Sir Walter Scott, and Robert Louis Stevenson. The university counts several heads of state and government amongst its graduates, including three British Prime Ministers. Three Supreme Court Justices of the UK were educated at Edinburgh, as were several Olympic gold medallists. As of October 2021, 19 Nobel Prize laureates, three Turing Award winners, two Pulitzer Prize winners, and an Abel Prize laureate and Fields Medalist have been affiliated with Edinburgh as alumni or academic staff.