Glusberg was born in Buenos Aires, Argentina, and was the longtime director of the Museo Nacional de Bellas Artes MNBA in Buenos Aires and co-director of Comité Internacional de Críticos de Arquitectura CICA. In 2002 he was leader of the Buenos Aires Biennale. He was one of the initiators of Centro de Arte y Comunicación CAYC, Buenos Aires, and was the director from 1968 until his death in early 2012.
Glusberg participated in the international architecture symposium "Mensch und Raum" (Man and Space) at the Vienna University of Technology (Technische Universität Wien) in 1984, which received much international attention. Other participants included Justus Dahinden, Pierre Vago, Bruno Zevi, Dennis Sharp, Frei Otto, Paolo Soleri and Ionel Schein. He wrote and edited several books about architecture, design and art in Latin America. He was a professor at New York University, Ball State University, National University of San Antonio Abad in Cuzco and University of Veracruz.
In 1981 he was highly distinguished with the Gold Medal from the Biennale in Sofia, Bulgaria and awarded the Jean Tschumi-Prize for Criticism by the International Union of Architects UIA. He was awarded Knight Commander of Peru (1981), Chevalier of the Ordre des Palmes Académiques (1987) and other distinctions.