Kliumuk attended the Leninski Komsomol Chernigov High Aviation School and entered the Soviet Air Force in 1964. The following year, he was selected to join the space programme.
He resigned from the cosmonaut team in 1978 to take up a position as the Assistant to the Chief of the Gagarin Cosmonaut Training Centre. In 1991 he was promoted to Chief of that facility and remained in that post until retirement in 2003.
Klimuk is a graduate of the Gagarin Air Force Academy and the Lenin Military Political Academy.
He holds an extensive and impressive range of awards, including Hero of the Soviet Union (twice), the Order of Lenin (three times), the Polish Order of Krest Grunvald, a Tsiolkovski Gold Medal, a Gargarin Gold Medal, and a Gold Medal from the Polish Academy of Sciences. He was made an honorary citizen of the cities of Kaluga, Gagarin, and Dzhezkasgan.
He is the author of two books on human spaceflight - Beside the Stars, and Attack on Weightlessness.