Gelitin lives and works in Vienna, Austria. Recent solo exhibitions include Museo Villa Croce, Genova, Italy (2018); Greene Naftali, New York (2017); Aspen Art Museum, Aspen (2014); Massimo De Carlo, Milan (2014); Tim Van Laere Gallery, Antwerp, Belgium (2013); Galerie Perrotin, Paris (2012); Kunsthalle Krems, Krems, Austria (2011); Musée d'Art moderne de la Ville de Paris, Paris, France (2008); and Deitch Projects, New York (2007).

Gelitin’s work is in the collections of Belvedere,Vienna
; MUMOK, Vienna; 
Thyssen-Bornemisza Art Contemporary (TBA21), Vienna;
 Essl Museum, Klosterneuburg, Austria; Lentos Kunstmuseum, Linz, Austria; MdM, Salzburg; Francois Pinault Foundation, Venice; Sammlung Falkenberg, Hamburg; 
Centre Pompidou, Paris; 
Musée d’art moderne de la Ville de Paris; La Maison Rouge, Paris; and MONA, Tasmania.