The university through alumni and academic staff is associated with some of the most significant intellectual and scientific contributions in human history. As of March 2019, 19 Nobel laureates have been affiliated with the university as alumni, faculty and researchers with 3 additional laureates acting as administrative staff including one of the fathers of quantum mechanics Max Born, theoretical physicist Peter Higgs, supramolecular chemist Sir Fraser Stoddart, biophysicist known for performing electron microscopy on biological molecules Richard Henderson and pioneer of in-vitro fertilisation Robert Edwards. Computer scientists Robin Milner and Leslie Valiant, both Turing Award laureates and mathematician Sir Michael Atiyah, Fields Medallist and Abel Prize winner, are associated with the university.

The university is further associated with scientists whose contributions include laying the foundations of Bayesian statistics (Thomas Bayes), nephrology (Richard Bright), the theory of evolution (Charles Darwin), the initial development of sociology (Adam Ferguson), modern geology (James Hutton), antiseptic surgery (Joseph Lister), classical theory of electromagnetism (James Clerk Maxwell) and thermodynamics (William John Macquorn Rankine); the discovery of carbon dioxide, latent heat and specific heat (Joseph Black), the HPV vaccine (Ian Frazer), the Higgs mechanism (Peter Higgs and Tom Kibble), the Hepatitis B vaccine (Kenneth Murray), nitrogen (Daniel Rutherford), chloroform anaesthesia (James Young Simpson) and SARS (Nanshan Zhong); and the inventing of the telephone (Alexander Graham Bell), the hypodermic syringe (Alexander Wood), the kaleidoscope (David Brewster), the telpherage (Fleeming Jenkin), the vacuum flask (James Dewar), the ATM (John Shepherd-Barron) and the diving chamber (John Scott Haldane).

Other alumni and academic staff of the university have included signatories to the US Declaration of Independence James Wilson, John Witherspoon and Benjamin Rush, Prime Ministers Gordon Brown, Lord Palmerston and Lord John Russell (the latter matriculated at Edinburgh, but did not graduate), Henry Dundas, 1st Viscount Melville, astronaut Piers Sellers, biologist Ian Wilmut, geologists Archibald Geikie and William Edmond Logan, physicists Sir David Brewster, John Robison and Peter Guthrie Tait, writers Sir Arthur Conan Doyle, Robert Louis Stevenson, J.M. Barrie, Sir Walter Scott, Aeneas Francon Williams and Alistair Moffat, economists Kenneth E. Boulding, James Mirrlees and John Hardman Moore, historian Sir Tom Devine, actor Ian Charleson, composers Kenneth Leighton, James MacMillan, and William Wordsworth, chemists William Henry, David Leigh, Guy Lloyd-Jones and Alexander R. Todd, botanist Robert Brown, surgeon James Barry, mathematician Colin Maclaurin, polymath Thomas Young, philosopher David Hume, pilot Eric "Winkle" Brown, former BP CEO Tony Hayward, former director general of MI5 Stella Rimington, theologians John Dickie and Robert Preus, former Home Secretary and Chancellor of the Exchequer Sir John Anderson, Spanish Civil War veteran and traditionalist Catholic writer Hamish Fraser, neurosurgeon B. K. Misra.

Olympic Games gold medallists from the university include six-times Olympic champion cyclist Sir Chris Hoy, rower Katherine Grainger and runner Eric Liddell.