Delatnost Muzeja počinje 1958. godine kad je aktom Saveta za kulturu Narodnog odbora grada Beograda doneta odluka o osnivanju Moderne galerije, ustanove čiji je zadatak bio da prati razvoj jugoslovenske savremene umetnosti. Izvršno veće SR Srbije odlučuje da za potrebe Moderne galerije sazida zgradu koja bi zadovoljila moderne muzeološke principe i određuje lokaciju na Novom Beogradu na ušću Save
u Dunav, naspram Beogradske tvrđave. raspisan je konkurs za idejno rešenje nove zgrade. Prihvaćen je projekat arhitekata Ivana Antića i Ivanke Raspopović za koji će im kasnije, na dan otvaranja Muzeja, biti dodeljena Oktobarska nagrada Beograda za arhitekturu. Po izgradnji nove zgrade, Savet Moderne galerije usvaja nov naziv ustanove – Muzej savremene umetnosti. Za prvog upravnika novog Muzeja postavljen je Miodrag B. Protić. U postavljanju osnova rada nove institucije uzeta su u obzir teorijska i praktična iskustva najuglednijih muzeja moderne i savremene umetnosti u svetu. Prilagođavajući se savremenim muzeološkim principima zaštite kulturnog nasleđa i politikama izlaganja, danas Muzej savremene umetnosti predstavlja dinamičnu instituciju koja obimom i raznovrsnošću svojih programa, istraživačkim i pedagoškim radom, intenzivnom međunarodnom saradnjom i otvorenošću za različite oblike kulturnih aktivnosti i saradnje, predstavlja važan činilac umetničkog i kulturnog života Beograda i Srbije koji, kao takav, igra i značajnu ulogu u procesima kulturnog preobražaja srpskog društva u periodu tranzicije i procesa evroatlantskih integracija. Osnivač i prvi direktor Muzeja savremene umetnosti (1965-1980) bio je Miodrag B. Protić, slikar i autor značajnih izložbi, knjiga i tekstova iz oblasti istorije jugoslovenske i srpske moderne umetnosti. Direktori Muzeja bili su: Marija Pušić (1980-1984), Kosta Bogdanović (v.d. direktora, 1984-1986), Zoran Gavrić (1986-1993), Radisav Trkulja (1993-2001) i Branislava Anđelković-Dimitrijević (2001-2013), Vladislav Šćepanović (v.d. direktora 2013-2014), Jovan Despotović (2014-2015), Slobodan Nakarada (v.d. direktora 2015-2020) i Viktor Kiš (v.d. direktora 2020-2021) i Marijana Kolarić (2021-).
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The Belgrade Museum of Contemporary Art was opened on October 20th 1965. However, Museum activities began as early as 1958, when an act brought by the Cultural Council of the Peoples’ Commitee of Belgrade established the Modern Gallery, an institution the purpose of which was to supervise the development of contemporary art in Yugoslavia. The Executive Council of the Socialist Republic of Serbia decided to construct a building which would live up to the standards of modern museological principles, and allots a location for it in New Belgrade, at the Sava-Danube junction, across the Belgrade Fortress. An open competition for the project of new building was announced in 1960. Architects Ivan Antić and Ivanka Raspopović won the competition with a project for which they would later, namely at the opening ceremony of the Museum, be awarded the October Prize of the City of Belgrade for Architecture. After the construction of the new building was completed, the Council of the Modern Gallery passes a new name for the institution – the Musem of Contemporary Art. The first director of the Museum was Miodrag B. The theoretical and practical experiences of the most distinguished international museums of modern and contemporary art were taken into consideration in the process of the creation of Museum’s guiding work principles. Staying in sync with contemporary museological principles of the conservation of cultural heritage and the politics of display, the Museum today represents a dynamic institution which by the scope and diversity of its program, by its research and pedagogical work, its intensive international collaboration and openness to diverse modes of cultural activity and cooperation, stands for an important factor of the cultural and art life of Belgrade and Serbia, which as such has been playing an important role in the processes of cultural transformation and Euro-Atlantic integration during the transitional period. Museum’s founder and its first director was Miodrag B. Protić, a painter and the author of many significant exhibitions, books and texts concerning the history of modern Yugoslav and Serbian art. The other directors of the Museum were: Marija Pušić (1980-1984), Kosta Bogdanović (executive director, 1984-1986), Zoran Gavrić (1986-1993), Radisav Trkulja (1993-2001), Branislava Andjelković Dimitrijević (2001–2013), Vladislav Šćepanović (acting director, 2013-2014), Jovan Despotović (acting director, 2014-2015) Slobodan Nakarada (acting director, 2015-2020), Viktor Kiss (acting director, 2020-2021) and Marijana Kolarić (2021-).