Kálmán Markovits was one of the players for the Hungarian water polo team that dominated the sport in the 1950s. With Markovits on board, the team claimed the 1952 and 1956 Olympic titles (adding bronze in 1960), and the 1954, 1958 and 1962 European titles. With Vasas, Markovits earned the Hungarian league title in 1953, and in 1951 he had been victorious at the World Student Championships. In 1966, he retired and completed his physical education studies. He was chosen as head coach of the Hungarian national team, eventually leading it to a bronze medal at the Mexico Olympics. While he was relieved from his Hungarian post, the Mexicans did want his services, and he was their national team coach until 1976. Markovits remained active as a coach in Mexico, Spain and Hungary through 1994, when he was inducted into the International Swimming Hall of Fame. Apart from Markovits himself, his relatives were also quite active in sports. His first wife, Katalin Szőke was a two-time Olympic swimming champion, and the daughter of Márton Homonnai, Olympic water polo champion in 1932 and 1936. He then married Márta Balogh, a World Champion in handball. Their son, László Markovits played professional tennis, and appeared in two Olympic games.