It has a national and international reputation for quality of exhibitions, projects and commissions, which are supported by a learning and engagement programme with audiences in excess of 100,000 each year.

[3] Adrian Searle of The Guardian commented, "Perhaps the museum bit was only ever there to confuse tourists and convince gowny academic Oxford that modern art was worth taking seriously.

Elliott introduced up-and-coming artists from Africa, Asia and the Soviet Union, and at various times also held major video art exhibitions.

He shifted the focus to exhibitions of contemporary artists, who have included Cecily Brown, Jake and Dinos Chapman, Tracey Emin, Gary Hume, Daniel Buren, Stella Vine, Sol LeWitt and Kerry James Marshall.

Artists' exhibitions have included Richard Long (1971); Sol Le Witt (1973) Joseph Beuys (1974); Donald Judd (1995); Marina Abramovic (1995, 2022–23); Carl Andre (1997), Lubaina Himid (2017), Ruth Asawa (2022), and Yoko Ono (1997).