He is director of research and programs, SALT , Istanbul, an institution that hosts almost 3,000 m2 (32,000 sq ft) of program space, a library of over 40,000 publications and some of the most important archives on Turkish contemporary and modern art, architecture and economy in the country with over 1,000,000 digitised items available for view. Kortun holds a position on the CIMAM  board for 2010 – 13; and is part of the board for Foundation for Arts Initiatives  (2009-). In 2011 Kortun served on the Tate Turner Prize selection committee. In 2013 he will curate the FOCUS on Turkey section of the Arco Art Fair in Madrid .
Kortun was founding director of Platform Garanti Contemporary Art Center, Istanbul, which he initiated in 2001. He was also founding Director of Project 4L, Istanbul Museum of Contemporary Art (2001–2003). Between 1994 and 1997 he worked as the founding Director of the Museum of the Center for Curatorial Studies, Bard College and received the 9th annual award for Curatorial Excellence from the Center for Curatorial Studies, Bard College in 2006.
Kortun has worked on a number of biennial projects such as: curator of the UAE Pavilion  for the Venice Biennale, 2001; co-curator of the Taipei Biennial  along with ManRay Hsu in 2008; Chief Curator and Director of the 3rd International Istanbul Biennial (1992) and Co-Director with Charles Esche of the 9th International Istanbul Biennial(2005); one of the curators of the Tirana Biennial, and 2nd Ceramics Biennial in Albisola, 2003. He curated the Turkish pavilions for the 1994 and 1998 São Paulo Biennial, and the 2007 Venice Bienniale for which he worked with artist Hüseyin Bahri Alptekin on an installation titled Don’t Complain.
He has undertaken numerous independent curatorial projects including most recently an exhibition of works by Cengiz Çekil  at Rampa  in Istanbul (2010) and he co-curated with November Paynter The Columns Held us Up at Artists Space, New York  (2009). He has written extensively on contemporary art and the cultural situation in Turkey for publications and periodicals internationally and in 2004 co-authored the book Jahresring 51: Szene Turkei: Abseits aber Tor on the Turkish art scene with Erden Kosova.