It is Russia's first state museum that specializes in art of the late 20th - early 21st centuries.
The museum was opened on December 15, 1999. It is housed in an estate of the late 18th century - the former mansion of Merchant Gubin was designed by architect Matvei Kazakov. The President of the Russian Arts Academy Zurab Tsereteli became the founder and the first director of the museum. Lots of exhibits in the museum collection were donated from his own private collection.
    The museum traces the main stages of the origin and further development of avant-garde art. The biggest part of the collection consists of Russian art works, though a considerable section is given to works by foreign artists. For example, the permanent exposition includes graphic art by Pablo Picasso, Fernand Leger, and Juan Miro, sculptures by Salvador Dalí, Armand, and Arnaldo Pomodoros, paintings by Henri Rousseau and Francoisa Gilles, and installations by the Japanese conceptualist Yukinori Yanagi.
    Works by classics of the Russian avant-garde of the early 20th century make the historical part of the museum collection. Lots of these exhibits were brought by Zurab Tsereteli back from abroad after being acquired at auctions and in prestigious galleries. These are canvasses by Kazimir Malevich, Marc Chagall, Natalya Goncharova, Mikhail Larionov, Lyubov Popova, El Lissitsky, Aristarkh Lentulov, Ivan Klyun, Olga Rozanova, Vladimir Tatlin, Robert Falk, Vasily Kandinsky, Pavel Filonov, Boris Grigoriev, Alexandra Exter, David Burliuk, Ilya Chashnik, Vladimir Baranov Rossine, Andrey Lansky, Léon Bakst and sculptures by Alexander Archipenko and Osip Tsadkin. The collection of works by the Georgian neo-primitive Niko Pirosmani is of special value.
    One of the exposition sections is dedicated to artists of the second wave avant-garde - i.e. nonconformism of the 1960s-1970s. These are works by masters nowadays widely known in Russia and abroad, namely Ilya Kabakov, Vladimir Nemukhin, Eduard Steinberg, Vladimir Yakovlev, Anatoly Zverev, Vitaly Komar and Alexander Melamid, Oscar Rabin, Marlen Shpindler, Mikhail Schwarzman, Dmitry Krasnopevtsev, Oleg Tselkov and others.
    Modern actual art of Russia is presented with paintings by Valery Koshlyakov, Vladimir Dubosarsky and Alexander Vinogradov, Victor Pivovarov, Sergey Shutov, and Yury Leyderman. Along with them the museum collection has installations, objects and photos by Oleg Kulik, Konstantin Zvezdochyotov, Francisko Infante, Igor Makarevich, Yuri Cooper, Vladislav Mamyshev-Monro, and Ilya Piganov.
Besides the main building the Moscow Museum of Modern Art has four other branches that are part and parcel of this museum: in Gogolevsky Boulevard and Tverskoy Boulevards, in Ermolayevsky Lane and in Bolshaya Gruzinskaya Street.