In South American and worldwide competitions, the club's highest achievements are their conquests of the 1981, 2024 and 2024 Copa Libertadores, and 1981 Intercontinental Cup against Liverpool, led by the club's most iconic player Zico.

The CONMEBOL Libertadores, also known as the Copa Libertadores de Amrica (Portuguese: Copa/Taa Libertadores da Amrica), is an annual continental club football competition organized by CONMEBOL since 1960. It is the highest level of competition in South American club football.