Solo shows of Carl Plackman have been held at various institutions across the UK, including the Arnolfini, Bristol; Huddersfield Art Gallery; Stanley Picker Gallery, Kingston Upon Thames; Chapter Arts Centre, Cardiff and Chisenhale Gallery, London. His work can be found in a number of prestigious permanent collections including the Tate Collection, Arts Council Collection, The Henry Moore Institute, Victoria and Albert Museum, British Museum, National Museum of Wales and the Art Gallery of New South Wales, Australia.