James VI of Scotland granted the charter in 1582. For its first 275 years, the university was governed by Edinburgh's town council, which had ultimate authority over staff appointments, curricula, and examinations. This produced friction. The late seventeenth and early eighteenth centuries were marked by a power struggle between the university and the council; in 1704 the council went so far as to seize the college records. The university expanded anyway, founding a Faculty of Law in 1707, a Faculty of Arts in 1708, and a Faculty of Medicine in 1726. In 1762, Reverend Hugh Blair was appointed by King George III as the first Regius Professor of Rhetoric and Belles-Lettres. This formalised literature as a university subject and made Edinburgh the oldest centre of literary education in Britain.

The university's structure produced its intellectual harvest. Unlike Oxford and Cambridge, Edinburgh was a single entity rather than a collection of loosely connected colleges; this encouraged the kind of academic exchange that creates new fields. It adopted the more flexible Dutch model of professorship, in which subjects had specialist teachers rather than each student cohort being shepherded by a single regent through everything. It had no land endowments, so professors operated competitively. Joseph Black isolated carbon dioxide and worked out latent heat. James Hutton looked at the rocks at Siccar Point and saw that the Earth was unimaginably old. Adam Smith wrote The Wealth of Nations. David Hume wrote his Treatise of Human Nature. Many taught alongside each other. Charles Darwin enrolled to study medicine here in 1825 but, finding the surgery without anaesthesia unbearable, left for Cambridge instead.

The university's eighteenth-century forte was teaching anatomy and the developing science of surgery, and Edinburgh's medical school was considered one of the best in the English-speaking world. The demand for cadavers created a darker market. Bodies for dissection were brought into the Anatomy Theatre through a secret tunnel from a nearby house, today's College Wynd student accommodation. During the 1820s, William Burke and William Hare used that same tunnel to deliver the corpses of sixteen people they had murdered for the fees the university paid. Hare turned king's evidence and lived; Burke was hanged in 1829 and then publicly dissected, ironically, in the very anatomy theatre his crimes had supplied. His skeleton is still on display at the university's anatomical museum.

In 1869, seven women led by Sophia Jex-Blake matriculated to study medicine at the University of Edinburgh. They were the first group of matriculated undergraduate women at any British university. The institution did not actually want them. The university blocked them from graduating and from qualifying as doctors. Their campaign drew national attention. They had Charles Darwin's support. Their effort put women's higher education on the national political agenda and led to the legislation that allowed women to study at all Scottish universities by 1889. Edinburgh admitted women to graduate in medicine in 1893. In 2015 the Seven were commemorated with a plaque. In 2019, almost a century and a half later, they were posthumously awarded their medical degrees. Their names: Sophia Jex-Blake, Isabel Thorne, Edith Pechey, Matilda Chaplin, Helen Evans, Mary Anderson, Emily Bovell.

Edinburgh produced laureates and revolutions. It also, on one occasion in 1838, produced a snowball fight that lasted two days. In what the press called the Edinburgh snowball riots, or the Wars of the Quadrangle, students started throwing snowballs at each other in a spirit of harmless amusement. The amusement spread. Local residents on South Bridge joined in against the students. The Lord Provost was forced to summon an infantry regiment from Edinburgh Castle to quell the disturbance. The students afterwards wrote a 92-page humorous account titled The University Snowdrop. In 1853, the English landscape artist Sam Bough painted the riot in watercolour. Universities have rarely required military intervention against snow.

In 1996 the Roslin Institute, which became part of the university's Royal (Dick) School of Veterinary Studies in 2008, cloned Dolly the sheep, the first mammal cloned from an adult somatic cell. The university also founded the Polish School of Medicine in 1941 as a wartime academic initiative for Polish doctors and students; 336 matriculated before its closure in 1949. The Royal (Dick) Veterinary College, founded by William Dick in 1823, became part of the university in 1951. The first department of nursing in Europe opened here in 1955. J. K. Rowling gave 10 million pounds in 2010 to create the Anne Rowling Regenerative Neurology Clinic. The Edinburgh Futures Institute opened in the converted Royal Infirmary buildings in June 2024. The university has educated three British Prime Ministers, sixteen Nobel laureates, two astronauts, and the founder of the medical schools at Columbia, Dartmouth, Harvard, McGill, Penn, and Yale. The town and gown survived their argument.