Following his first institutional solo exhibition in 1972 at the Whitechapel Gallery, London, Woodrow went on to represent Britain at Biennales in Sydney (1982), Paris (1982, 1985) and São Paulo (1983). He was shortlisted for the Turner Prize in 1986 and participated in Documenta 8, Kassel in 1987. He was elected a Royal Academician in 2002 and had a major retrospective at the Royal Academy of Arts, London in 2013. His sculpture, Celloswarm (2002), was included in the Frieze London 2019 Sculpture Park. A similar piece, Clockswarm (2001), was on view in The Box at Pippy Houldsworth Gallery concurrently.
Selected solo exhibitions include those at Modern Art Oxford (1983); ICA, Boston (1985); The Fruitmarket Gallery, Edinburgh (1986); Tate, London (1988 and 1996); Seattle Art Museum (1988); Chisenhale Gallery, London (1993); Camden Arts Centre (1995); South London Gallery, London (2001) and Yorkshire Sculpture Park (2005). The Ledge, a large-scale public artwork, initially commissioned for the Folkestone Triennial (2017), was acquired permanently by Folkestone Artworks, the UK’s largest urban outdoor contemporary art exhibition.
Woodrow’s work is held in numerous public collections including Museum of Modern Art, New York; Metropolitan Museum of Art; New York; Moderna Museet, Stockholm; Tate, London; British Museum, London; British Council, London; Hirschhorn Museum and Sculpture Garden, Washington; Fundação Calouste Gulbenkian, Lisbon; Museum of Contemporary Art, Chicago; Museo Tamayo, Mexico City; Scottish National Gallery of Modern Art, Edinburgh; Victoria & Albert Museum, London; Musée d’Art Contemporain, Montreal and Kunsthaus Zürich amongst many others.