Stoschek first began buying art in 2003. Her collection features works by mainly European and US artists working from the 1960s onwards and includes video, multi-media environments, internet-based installations and performance. The Julia Stoschek Collection in a former industrial building in Düsseldorf-Oberkassel opened in 2007, and has two floors of exhibition space, over 2,500 square metres (27,000 square feet). Since the opening, she has mounted regular collection-based shows, including solo exhibitions on Cyprien Gaillard and Bruce Nauman.
Stoschek also is the vice chair of the Kunst-Werke Institute for Contemporary Art after being a member of the board for several years. In 2016, she opened a satellite exhibition space in a former Czech cultural center in Berlin.