Klimkin was born on 15 August 1980 in Moscow, Russian SFSR, Soviet Union.

[1] Klimkin's grandmother introduced him to skating at the age of four because she felt it would be good for his health.

[1] At the 1999 Nebelhorn Trophy, Klimkin became the first skater to land two different quadruple jumps in one program, which he did by landing a quad salchow and a quad toe loop in the free skate.

[1] In the summer of 2003, Klimkin had a calf injury which became infected and required three surgeries; he returned to the ice in late September and won 2002 NHK Trophy two months later.

He announced his retirement from competitive skating on 19 April 2007.