Murphy's first solo exhibition, 'Britney Love' was held in 2000 at Canberra Contemporary Art Space, following a residency there. Other solo exhibitions include 'Lift', BREENSPACE, Sydney, (2013); 'Kate Murphy: Probable Portraits', Shepparton Art Museum (2013); 'The note', BREENSPACE, Sydney (2010); 'Cry me a future', National Portrait Gallery, Canberra (2009); 'Rehearsal (for Saint Vitus)', Virgin Mary Church, Dublin (2007); and 'Placing the Camera', Performance Space, Sydney, (2005).Murphy has exhibited nationally and internationally including; '24 Frames Per Second', CarriageWorks, Sydney (2015); 'Resonant Actions', CACSA, Adelaide (2014); 'Volume One: MCA Collection', MCA, Sydney (2012); 'Here’s the Tender Coming (WHOOPEE) We’re all Going to Die', Pallas Projects, Dublin (2011); TWMA Contemporary 2010, TarraWarra Museum of Art (2010); 'Nightshifters', Performance Space (2010); 'Video Swell Sydney', AGNSW (2009); 'Rising Tide: Film and Video Works from the MCA Collection', MCA, Sydney and San Diego (2009); 'Contemporary Australia: Optimism', GOMAt, Brisbane (2008); 'Sonic Youth', Green on Red Gallery, Dublin and Amelie A Wallace Gallery, New York; (2008); 'Interlace', Performance Space, Sydney and CAST Gallery, Hobart (2004); and 'Remembrance + the Moving Image', ACMI, Melbourne (2003). Murphy’s video works have also been screened at the Barbican, London (2011); LOOP’08, Barcelona (2008); Broadstone Gallery, Dublin (2007); Foundation for Art and Creative Technology (FACT), Liverpool (2006); and National Gallery of Australia, Canberra (2004). Murphy won the 2004 Helen Lempriere Travelling Art Scholarship, which she undertook in 2006, travelling to the UK and Ireland. She has been the recipient of numerous grants and residencies including an Australia Council for the Arts residency at the Greene Street studio in New York (2007) and the Fire Station Artists’ Studios in Dublin (2006).