"Babyface" was written by Bono during the Zooropa recording sessions in late 1992/early 1993. The song contains themes of desire, voyeurism, image, celebrity and technology. It involves a man having an obsession with a famous woman, whose image he keeps on a televised recording. During the production, U2 and producer Brian Eno incorporated a toy piano into the melody of the song.
"Babyface" received mixed reviews from critics. The New York Times critic Jon Pareles described the song as U2 combining "'With or Without You' and Bowie's 'Ashes to Ashes'" while praising the "tinkling countermelody" of the song.The Boston Globe's Jim Sullivan called it "the most conventional song" on the album and "a smooth-glider where the subversiveness is half-buried in the rolling rhythms and the soft, seductive melody." In contrast, Parry Gettelman of Orlando Sentinel felt the song was "tediously repetitive" and caused the album to falter.
After the release of Zooropa, several of the album's songs were incorporated into the Zoo TV Tour setlist. Babyface was only played five times on the European Zooropa leg of the tour. It made its debut at London's Wembley Stadium on August 11, 1993. However, as with other Zooropa songs, U2 found it difficult to perform it live onstage. After its first performance, Bono joked the band had the "nice idea" of putting such songs on the record and having to play them as a result. The song was dropped from the setlist after the August 20 concert and has never been played since.