Aguirre was born in Mexico City on 1 December 1958, and nicknamed El Vasco as his parents were both from the Basque Country of Spain.

Following a short period with the Los Angeles Aztecs, he returned to Club América, contributing to their championship victory in the 1983–84 season by scoring in the final.

[2] He played in the FIFA World Cup on home soil in 1986, and was sent off in the quarter-final defeat to West Germany; the game went to penalties after a 0–0 draw.

[5] In his first game on 1 July, El Tri beat rivals the United States at home with a single Jared Borgetti goal.

[8] A year later at the 2002 World Cup in South Korea and Japan, his side won their group at Italy's expense before losing 2–0 to the US in the Round of 16.

[10] In his first season in Pamplona, the club reached the semi-finals of the Copa del Rey, losing 4–2 on aggregate to Recreativo de Huelva.

[13] On 24 May 2006, days after Osasuna finished the season in fourth, Aguirre signed a one-year contract to replace Pepe Murcia at Atlético Madrid.

[16] On 3 April 2009, Aguirre was officially appointed as the new manager of the Mexico national team, replacing Sven-Göran Eriksson.

[18] Aguirre apologized to the Mexican fans, media, football players and staff, but never extended such courtesy to Philips or the Panamanian team.

On 30 June 2010, Aguirre resigned as coach of Mexico following their failure to reach the quarter-finals of the 2010 FIFA World Cup in South Africa.

Mexico finished second in Group A, ahead of hosts South Africa and France, but their progress was halted in the round of 16 where they were defeated 3–1 by Argentina.

[24] During the run up to the World Cup Aguirre expressed his desire to coach in the Premier League in England, but did not receive any offers.

[29] In August 2014, Aguirre became the new manager of the Japan national team, replacing Alberto Zaccheroni, who had resigned following the World Cup.

[30] At the 2015 AFC Asian Cup, Japan won all three of its group matches, scoring seven goals and conceding none, though was knocked out in the quarter-final by the United Arab Emirates.

[32] On 21 May 2017, after leading Al Wahda to the President's Cup championship victory, Aguirre decided to step down as manager.

[42] On 24 March 2022, Aguirre returned to La Liga, joining Mallorca, who were one point inside the relegation zone with nine games to go.

[47] In November 2024, Aguirre was hit by a beer can, leaving him bloodied after his team’s 2-0 loss to Honduras in the Nations League quarter-final.