- 43 appearances for Argentina National Football Team (1973-1982); scored 20 goals; won the 1978 FIFA World Cup.
- Scored 2 goals for Argentina against Netherlands during th final match of World Cup Argentina 1978.
- Striker for Instituto A.C.C. (1972-73), Rosario Central (1974-1976), Valencia C.F. (Spain, 1976-1981, 1982-1984), River Plate (1981-82), Hércules (Spain, 1984-1986), First Vienna (Austria, 1986-87), St. Pölten (Austria, 1987-1990), Kremser SC (Austria, 1990-1992), C.D. Arturo Fernández Vial (Chile, 1995) and Pelita Jaya (Indonesia, 1996).
- Top Scorer of the Argentine Primera División (1974 & 1976), La Liga (1977 & 1978) and the UEFA Cup Winners' Cup (1980).
- Father of, with Mavi Moll, Arianne Kempes, Magalí Kempes and Mario José Kempes.
- Honours with Valencia C.F.: Copa del Rey (1979); UEFA Cup Winners' Cup (1980); UEFA Super Cup (1980). Honours with River Plate: Primera División (1981 Nacional).
- Retired from football in 1996.
- Father, of with Julia, Natasha Kempes and Nicole Kempes.
- Rosario Central's all-time top scorer (107 goals).
- Named the South American Footballer of the Year in 1978.
- Over his entire career, he officially scored 367 goals in 649 matches.
- Played well over 200 games for Valencia C.F..
- Played well over 200 games at La Liga.
- Broken Juan Costa record on the Valencia C.F.'s list of the all-time top goalscorers with 149 goals.
- Played well over 100 games at Austrian Bundesliga.
- Golden Boot and Golden Ball at the 1978 FIFA World Cup.
- Won the 1978 Onze d'Or.
- Named the Argentine Footballer of the Year in 1978.
- Head coach of Lushnja (Albania, 1996), Mineros de Guayana (Venezuela, 1997-98), The Strongest (Bolivia, 1999), Blooming (Bolivia, 2000), Independiente Petrolero (Bolivia, 2000-01), Casarano (Italy, 2001-02) and San Fernando (Spain, 2002).
- He was the first foreign manager who signed a foreign player in Albanian football history.
- Thanked by Diego Maradona in the liner notes of their autobiography "Yo soy el Diego" (2000).
- 2004: One of FIFA 100 by Pelé.
- Ranked #23 in the 2006 IFFHS list of the "South American Player of the Century".
- Won the 2007 Golden Foot as football legend.
- Works as analyst and commentator for ESPN Deportes (USA).
- The Córdoba stadium was named after him since 2010.
- 2015: Named in the AFA Team of All Time.
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