at the 2011
Rock in Rio Festival in
Rio de Janeiro, Brazil. In 1995, after opening for Spanish singer-songwriter
Joaquín Sabina at a concert at the
Teatro de Verano in
Montevideo, Drexler was invited to
Madrid by Sabina, who introduced him to other prominent musicians in the Spanish music scene. In Spain, Drexler recorded the album
Vaivén in 1996 with Spanish musicians.
Vaivén included some old songs from his previous releases mixed with new compositions. He moved to Spain and recorded another four albums:
Llueve (1997),
Frontera (1999),
Sea (2001) and
Eco (2004). In 2001, Drexler co-wrote two songs for Spanish singer
Rosario Flores ("Agua y Sal" and "Rosa y Miel") for her album
Muchas Flores. Drexler's song "
Al Otro Lado del Río" appeared in the internationally acclaimed film
The Motorcycle Diaries. Though Drexler himself sang the song on the movie soundtrack, he was not allowed to perform the song at the
2005 Academy Awards, since "he was not popular enough," according to Spanish newspaper
El País; Spanish actor
Antonio Banderas and Mexican-American musician
Carlos Santana sang the track instead. Upon winning, Drexler recited two verses of the song at the podium. Drexler became the first Uruguayan to win an Academy Award. After that, he released
12 Segundos de Oscuridad (2006); this album contained ten original songs and two covers: "
High and Dry" from British band
Radiohead and "Disneylandia" from Brazilian
Titãs. Although he lives most of the year in Spain, his albums were partially recorded in Uruguay with Uruguayan musicians.
Juan Campodónico and
Carlos Casacuberta, former members of rock band
El Peyote Asesino, had produced Drexler's albums from
Frontera to
12 Segundos De Oscuridad. In 2008, he released a double live album, recorded in different concerts in Spain:
Cara B (2008), mainly filled with songs previously unreleased. During 2009, Drexler worked with Colombian performer
Shakira on the Spanish-language versions of her singles "
She Wolf", "
Did it Again" and "
Waka Waka (This Time for Africa). Drexler recorded
Amar la Trama (2010) on November 1–4, 2009 in Madrid, Spain in just four days, with musicians playing live on studio.
Amar la Trama was recorded in a television studio in front of a small audience who were selected in an online contest. He chose this format to avoid the "coldness" of the
recording studio. His album
Bailar en la Cueva, released in 2014, marked a stylistic shift toward more rhythm-focused and dance-oriented music. Drexler has described the album as contrasting with his earlier works, which he characterized as more introspective and nostalgic. He has also stated that it differs significantly from his previous album, referring to it as the “opposite pole” of
Amar la Trama. In 2017, he released
Salvavidas de Hielo, an album constructed entirely from sounds produced by guitars and the human voice, including percussion effects.
Tinta y Tiempo was released in 2022. His music is a combination of Uruguayan traditional music (
candombe,
murga,
milonga,
tango),
bossa nova,
pop,
jazz and
electronic music. The words also play an important role in his songs. Apart from love, reflections about identity, race and religions are a constant in his work. ==Personal life==