The museum stands on the site of the old Fort Thüngen, on the southwestern edge of the Kirchberg-plateau, in close proximity to many of the European Union institutions based within the city.

[3] The museum was inaugurated on 1 July 2006 by Grand Duke Jean, to whom the building is dedicated, and opened to the public the following day.

As Luxembourg had no public modern art collection and the museum budget did not allow acquiring a modernist collection, the museum focused on contemporary art – its permanent collection includes works by 100 artists, including: Andy Warhol, Bruce Nauman, Julian Schnabel, Thomas Struth, and Daniel Buren.

[3] Under the direction of Marie-Claude Beaud,[4] in its first year of public opening, the museum achieved a record attendance of more than 115,000 visitors.

The Museum's collections are set out on three floors and include works by many artists and designers such as Alvar Aalto, Marina Abramović, Bernd and Hilla Becher, Pierre Bismuth, Sophie Calle, Hussein Chalayan, Claude Closky, James Coleman, Tony Cragg, San Damon, Richard Deacon, Mark Dean, Stan Douglas, Jan Fabre, Ian Hamilton Finlay, Roland Fischer, Günther Förg, Gilbert & George, Nan Goldin, Andreas Gursky, Peter Halley, Thomas Hirschhorn, Fabrice Hybert, Suki Seokyeong Kang, William Kentridge, Mark Lewis, Richard Long, Michel Majerus, Christian Marclay, Martin Margiela, Steve McQueen, Bruce Nauman, Shirin Neshat, Albert Oehlen, Blinky Palermo, Philippe Parreno, Grayson Perry, Fiona Rae, Pipilotti Rist, Thomas Ruff, Charles Sandison, Joe Scanlan (artist), Thomas Scheibitz, Julian Schnabel, Cindy Sherman, Thomas Struth, Wolfgang Tillmans, Cy Twombly and Kara Walker.