Levon Julfalakyan was active in gymnastics before taking up wrestling. Julfalakyan had a very brief wrestling career, but he still managed to win the three most important major titles: Olympic, World, and European. Wrestling in the Greco-Roman lightweight class his entire career, Julfalakyan was Olympic Champion in 1988 and World and European Champion in 1986. He also won the 1985 World Cup, the 1984 European junior title, and bronze at the 1989 World Championships. Julfalakyan never captured a Soviet title, but earned silver (1985) and bronze (1984) at the Soviet Championships. After finishing his sporting career, Julfalakyan worked as a wrestling coach. Since 1999 he has been head coach of the Armenian national Greco-Roman team and, in 2002, became vice-president of the Armenian Wrestling Federation. Julfalakyan has also been president of the Armenian Olympians Association and a member of the executive committee of the Armenian National Olympic Committee.