This album marked a turning point as it was his first production under the WEA Latina label, an important step in his career. The recording took place between November and December 1990 at Quarzo Studios in Madrid, Spain, and the result was a Latin pop album with a total duration of 42 minutes and 10 seconds. Under the production of Miguel Ángel Arenas, Sanz composed all the songs, though initially he signed them under the pseudonym A. Medina, a name he had already used at the beginning of his career.
Viviendo Deprisa catapulted Alejandro Sanz to national recognition in Spain. Several of his songs resonated strongly, with the singles "Los Dos Cogidos de la Mano" and "Pisando Fuerte" standing out, not only becoming hits but also having their own music videos. Other tracks that caught the attention of radio stations included "Se Le Apagó la Luz" and "Lo Que Fui Es lo Que Soy". The album, which contains ten songs in total, was completed with tracks such as "Todo Sigue Igual", "Viviendo Deprisa" (which gives the album its title), "Duelo al Amanecer", "Completamente Loca", "Toca Para Mí", and "Es Este Amor".
In 2006, an expanded edition of the album was released, titled Viviendo Deprisa (Edición 2006). This reissue included a CD with three additional tracks and a DVD containing six music videos, offering a new perspective on this work that remains a reference in Alejandro Sanz's discography.