He founded his first own gallery in 1972 in its original Cologne Lindenstraße 20 Galeriehaus location, debuting with an Yves Klein solo exhibition of his Anthropometry series.
In 1980 the gallery moved into the former space of Aenne Abels at Wallrafplatz 3 exhibiting Cy Twombly (1982),[4] Lucio Fontana (1982 and 1983)[5] and Willem de Kooning (1990)[6] among others.
The space was inaugurated with a John Chamberlain solo show, followed by Josef Albers (1996 and 1998),[7] Cy Twombly (1997),[8][9][10] Wols (1998), Louise Bourgeois (1999) and Jannis Kounellis (1999) exhibitions.
[1][12][13] In 1994, Karsten Greve opened a third gallery space in the Via Santo Spirito in Milan in the historical city centre near Via Montenapoleone, dedicating the first show to Cy Twombly.
[14] Among the artists exhibited were Piero Manzoni, Lucio Fontana, Alberto Burri, Nicola de Maria, Osvaldo Licini, Francesco Lo Savio.
[19][20][21][22][9][23] Karsten Greve's longstanding friendships with many represented artists such as Cy Twombly, Louise Bourgeois, John Chamberlain,[24] Jannis Kounellis, Pierre Soulages and Gotthard Graubner provided the basis for the gallery's programme.
[26][19][27] The gallery's main focus lies in major renewal movements present in the international art world after 1945, which provided the impetus for the continuation of revolutionary Modernism emerging after the turn of the century.
The gallery stages solo and group exhibitions in its own exhibition spaces and also in collaboration with major international museums and other non-commercial art institutions, working closely with the Centre Pompidou in Paris, the Guggenheim Museum in New York, the Nasher Sculpture Center in Dallas, the Fondation Beyeler and the Kunstmuseum Basel among others by contributing works as loans.
[38] Highlights from the gallery's publishing activities include the following titles produced: BRASSAÏ – DUBUFFET (2011), Joseph Cornell, (1992) including texts from Joseph Cornell's journals, Louis Soutter, Finger-paintings 1937-1942, (1998), with texts by Jean Dubuffet, Lucio Fontana, Sculpture/Skulptur, lo sono uno scultore e non un ceramista, Catalogue III (2012) and Cy Twombly, Work on Paper, Catalogue VI (2013).