A Portuguese international, he amassed 94 caps and scored 26 goals for A Seleção and represented the country in three UEFA European Championships and one FIFA World Cup.

On 27 September 2001, Costa scored his first goal for Milan to open a 4–0 home win (6–0 aggregate) in the first round of the UEFA Cup against BATE Borisov.

[17] Ahead of his second season at Milan, Costa's faced competition from Brazilian new signing Rivaldo, but secured a starting place against him.

[17] On 24 September 2002, he assisted three goals in a 4–0 Champions League group win at Deportivo de La Coruña, leading a television commentator to call him three times better than Zinedine Zidane.

[17] He scored his first domestic goal on 18 December, equalising in a 5–1 win (6–2 aggregate) against Ancona at the San Siro in the second leg of the last 16 of the Coppa Italia.

[18] In the 6–3 aggregate final win over Roma in May, he played only 30 minutes as a substitute as Brazilians Rivaldo and Serginho were preferred in attacking midfield.

[19][20] This was to rest him for the 2003 UEFA Champions League Final against Juventus, in which he was substituted injured for Massimo Ambrosini near the end of regulation time in a goalless draw that the Rossoneri won on penalties at Old Trafford.

[25] He had been released from Milan, after both the player and the club reached an agreement to end his €4.6 million per year contract, in order to fulfill his long-held dream of returning to Benfica.

Costa was part of the Portugal national under-20 team under manager Carlos Queiroz who won the 1991 FIFA World Youth Championship on home soil.

[36] On 31 March 1993, Costa made his debut for the senior national team in a 1–1 draw away to Switzerland, in 1994 FIFA World Cup qualification.

While being substituted, he was shown a red card by referee Marc Batta for leaving the pitch too slowly, meaning that Portugal could not bring Sérgio Conceição on as a replacement.

[43][44] At the finals in Belgium and the Netherlands, he assisted the last two goals by João Pinto and Nuno Gomes in a 3–2 comeback win over England in a run to the semi-finals.

Costa was dropped for Pinto after a shock 3–2 opening loss to the United States, but came on as a substitute in the next game and finished Capucho's cross to conclude a 4–0 win over Poland.

[49] In the quarter-finals against England, again as a substitute, he scored a long-range goal in extra time as the game finished 2–2 and went to penalties; he missed in the shootout but his team prevailed.

[52] Costa is considered by pundits to have been one of the greatest midfielders both of his generation, as well as one of Portugal's best players ever, and was regarded as one of the best playmakers in the world in his prime.

A quick, technically gifted and elegant player, throughout his career, he was renowned for his excellent dribbling skills, close control, intelligent movement, vision, and precise passing, which made him an effective assist provider, and enabled him to create space for his teammates, or orchestrate his teams' attacking moves.

During the summer 2008 transfer window, Costa brought head coach Quique Sánchez Flores, playmaker Pablo Aimar, winger José Antonio Reyes, and striker David Suazo, the latter two on loan.

[74] For the 2020–24 quadrennial, he became a vice-president of the club's board of directors, as part of Luís Filipe Vieira's list for a sixth consecutive mandate.

[86] After signing with Roger Schmidt, Benfica's first non-Portuguese manager since Flores, the club won the 2022–23 Primeira Liga, ending a four-year trophy wait.