His emigration to France in 1947 made him a persona non grata in Yugoslavia, but has also made possible for him to show the world his class, that has later earned him the title of one of the greatest ballet dancers in the world in the 1950s. His greatest successes include the roles of Prometheus, Don Juan, Tristan, Hamlet, and Orestês. He has worked with some of the most famous artists of his time, such as choreographer Serge Lifar, opera singer Maria Callas, as well as the world's most prominent ballerinas of his time, such as Zizi Jeanmaire, Yvette Chauviré, Margot Fonteyn and Alicia Markova. In 1956, he founded his own company, which continued to tour for ten years. In 1966, Mišković performed in Yugoslavia for the first time after his emigration.
Since the end of his professional career, he began to work with UNESCO, first as an art director, and later he became the honorary president of UNESCO International Dance Council.
In 2009, Serbian director Ivan Jovanović made a film about Mišković's 60 years long professional career, entitled A Leap into the infinity.
Mišković was married to Nita-Carol Cervin.
