Eurythmics' commercial breakthrough came with Sweet Dreams (Are Made of This) (1983 in music), whose hit single of the same name featured a dark, powerfully sequenced synth bass line and a striking video that introduced the orange crew cut Lennox sported to fame.

The band's fortunes changed immensely from this moment on. The album became a huge British hit due to the title track, which quickly topped the American charts as well. Lennox was featured on the cover of Rolling Stone magazine. Stewart recently revealed that the famous synth bass line in the song was discovered by accident when he inadvertently played a track backwards.

"Love Is A Stranger" was re-released and became a hit in its own right. The "Love Is A Stranger" video saw Lennox in many different character guises, which she later became known for in subsequent videos ("Beethoven" and "The King & Queen of America" among them).

The album's working title was Invisible Hands (as was a track left off the album), inspiring the name of UK indie label Invisible Hands Music - known for releasing music by Hugh Cornwell, Mick Karn and Hazel O'Connor. In January 1985 both Lennox and Stewart, plus their manager Kenny Smith, were featured on the cover of the inside-business world distributed magazine Music Management & International Promotion.

Touch, the rapid follow-up to Sweet Dreams (Are Made of This), was released in late 1983 and spawned three major hits. Here Comes the Rain Again (number four in the U.S.) was an orchestral/synth ballad (with orchestrations by Michael Kamen) that led the album. The video went into heavy rotation on MTV.

"Who's That Girl?" was also a massive hit, the video seeing Lennox as a blonde chanteuse and featured cameos by Hazel O'Connor, Bananarama (including Stewart's future wife, Irish born singer Siobhan Fahey), Kate Garner of Haysi Fantayzee, Thereza Bazar of Dollar, Jay Aston and Cheryl Baker of Bucks Fizz, Kiki Dee, Jacquie O'Sullivan and "gender-bending" pop singer Marilyn, among others. The upbeat, calypso-flavored "Right By Your Side" showed a different side of Eurythmics altogether, and Touch solidified the duo's reputation as being major talents and cutting edge musicians.

In 1984, RCA released Touch Dance, a mini-album of remixes of four tracks from Touch, aimed at the 'club market'. The remixes were by prominent New York name producers François Kevorkian and John "Jellybean" Benitez.

Also released in 1984, the Eurythmics soundtrack album 1984 (For the Love of Big Brother). Virgin Films had contracted the band to provide a soundtrack for Michael Radford's modern film adaptation of George Orwell's Nineteen Eighty-Four. Radford later said that the music had been "foisted" on his film against his wishes, and that Virgin had replaced most of Dominic Muldowney's original orchestral score with the Eurythmics soundtrack (including the song "Julia", which was heard during the end credits).

However, the record was presented as "music derived from the original score of Eurythmics for the Michael Radford film version of Orwell's 1984". Eurythmics charged that they had been misled by the film's producers as well, and the album was withdrawn from the market for a period while matters were litigated.

The album's hit single, "Sexcrime (Nineteen Eighty-Four)", was huge in the UK, Australia and in Europe, and a major dance hit in the United States, but its supposedly suggestive title (actually taken from the "Newspeak" phrase used in Orwell's book) resulted in many U.S. pop radio stations refusing to play the track.