Honours
Club
- Primera División: 1981
- Copa del Rey: 1983
- Copa de la Liga: 1983
- Supercopa de España: 1983
Country
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- FIFA World Youth Championship: 1979
- FIFA World Cup:
- Artemio Franchi Trophy: 1993
- 75th anniversary FIFA Cup: 1979
Individual
- Golden Ball for Best Player of the FIFA U-20 World Cup: 1979
- Argentine league Top Scorer: 1979, 1980, 1981
- Argentine Football Writers’ Footballer of the Year: 1979, 1980, 1981, 1986
- South American Footballer of the Year (El Mundo, Caracas):1979, 1986, 1989, 1990, 1992
- Italian Guerin d’Oro: 1985
- Argentine Sports Writers’ Sportsman of the Year: 1986
- Golden Ball for Best Player of the FIFA World Cup: 1986
- L’Équipe Champion of Champions – 1986
- United Press International Athlete of the Year Award: 1986
- Best Footballer in the World Onze d’Or: 1986, 1987
- World Player of the Year (World Soccer Magazine): 1986
- Capocannoniere (Serie A top scorer): 1987–88
- Golden Ball for services to football (France Football): 1996
- Argentine Sports Writers’ Sportsman of the Century: 1999
- Marca Leyenda: 1999
- Argentine Senate “Domingo Faustino Sarmiento” recognition for lifetime achievement:
- “FIFA Goal of the Century” (1986 (2–1) v. England; second goal): 2002
- FIFA Player of the Century