Born in Uzbekistan to a Crimean Tatar family, Rustem Kazakov took up wrestling in 1959. Kazakov wrestled in the Greco-Roman bantamweight class throughout his career and made his international début at the 1967 European Championships, where he won a bronze medal. Next Kazakov competed at the 1967 World Championships, where he was seventh, and was also scheduled to wrestle at the 1968 Olympics, but had to withdrew at the last minute due to fractured ribs sustained in training. After the 1968 Olympics, Kazakov won World titles in 1969 and 1971, while taking bronze at the 1970 World Championships, and went to the 1972 Olympics as a clear favorite for the Greco-Roman bantamweight title. The Olympics did not start very successfully for Kazakov, however, as he lost by decision to Khristo Traykov in the second round. He then won his remaining four matches, however, two of them by fall, to win gold. After the Olympics, Kazakov won silver at the 1973 World Championships. but then retired from sports in 1975. Domestically, Kazakov was not as successful as he was internationally, winning only one Soviet title in 1971. After finishing his sporting career, Kazakov worked as a wrestling coach with CSKA Moskva and was also the coach for the Soviet national team. In 1989 Kazakov moved to Crimea, Ukraine, where his family originated, and became the president of the Crimean Kurash Federation, a traditional Tatar style of wrestling. Since 2001, an annual Greco-Roman tournament in his honor has been held in Alushta, Crimea, Ukraine.