Kempes was nicknamed El Matador (The Bullfighter) from his time with Valencia, he won two consecutive Pichichis, scoring 24 and 28 goals in 1976-77 and 1977-78. His career where started at a local club called Instituto Atlético Central Córdoba before quickly moving on to Rosario Central where he gained 85 goals in just 105 matches and established himself as a notorious goalscorer. Famous as a hard-working forward, he used to strike from outside the penalty area with his surging runs goalwards and was not the traditional center-forward operating solely inside the box. Many defenders found difficulties handling his attacking style. They never knew where they had him.
Before the 1978 World Cup, Kempes was the only foreign based player on the list of coach César Luis Menotti's national team in Argentina. The coach described him when announcing the squad he had selected for the 1978 tournament, "He's strong, he's got skill, he creates spaces and he shoots hard. He's a player who can make a difference, and he can play in a centre-forward position".
The skinny forward had been topscorer in La Liga in each of the past two seasons and was determined to show on home soil that he could deliver against the best on the sport's greatest stage as well. However, in 1974, at 20 years of age, he failed to get on the score-sheet in West Germany and after the first round groupstage in 1978, his name was still missing among goalscorers in the tournament. During his playing career he won 43 caps for Argentina and scored 20 times. He represented his country in three World Cups in 1974, 1978 and 1982, winning the competition in 1978. He was the leading goalscorer in the 1978 tournament, scoring six goals. He has also scored some very important goals for Argentina in his career.
In 1978 he was named South American Football Player of the Year ("El Mundo", Caracas, Venezuela). He was named by Pelé as one of the top 125 greatest living footballers in March 2004.
Kempes made his first title as coach came in 1999 with The Strongest (Bolivia), before he moved to another Bolivian club, Independiente Petrolero. Before then, he worked as assistant to their Uruguayan coach Héctor Núñez in Valencia, and as a player-manager of Indonesian Leaguechampions Pelita Jaya before hung up his boots for the last time at the age of 41 in 1996. He is currently an analyst on ESPN Deportes.