[6] Rolling Stone called the song "a synth-pop masterpiece that made Lennox and Dave Stewart MTV superstars".

On Rolling Stone's The 500 Greatest Songs of All Time issue in 2003, "Sweet Dreams (Are Made of This)" was ranked number 356.

[13] According to Lennox, the lyrics reflected the unhappy time after the breakup of the Tourists, when she felt that they were "in a dream world" and that whatever they were chasing was never going to happen.

Stewart thought the lyrics too depressing and added the "hold your head up, moving on" line to make it more uplifting.

'"[13] "Sweet Dreams (Are Made of This)" was created and recorded in two places, first in Eurythmics' tiny project studio in the attic of an old warehouse in the Chalk Farm district of north London where they were living at the time, then in a small room at The Church Studios in north London.

[11][14] The home studio was equipped with a Tascam 80-8, 8-track half-inch tape recorder, a Soundcraft mixer, a Roland Space Echo, a Klark Teknik DN50 spring reverb, a B.E.L.

[14] Also purchased with the bank loan was a £2000 Movement Systems Drum Computer, one of only about 30 built, with the band having to sleep for a few days at the Bridgwater apartment of the manufacturer while their early prototype unit was being assembled.

To fill out the complement of instruments, Lennox played a borrowed Oberheim OB-X for sustained string sounds.

Their only microphone, a utilitarian model typically used for hi-hat, performed all the acoustic duties, including tracking Lennox's vocals.

After a radio DJ in Cleveland kept playing the song from the album, and it generated a strong local response, RCA decided to release it in the US.

[13] The video received heavy airplay on the then-fledgling MTV channel and is widely considered a classic clip from the early-MTV era.

[7] The video begins with a fist pounding on a table, with the camera panning up to reveal Lennox in a boardroom, with images of a Saturn V launch projected on a screen behind her, which are later replaced by a shot of a crowd walking down a street.

The video ends with Lennox lying in bed, with the last shot being a book on a nightstand bearing a cover identical to the album.

The BBC stated her "powerful androgynous look" was the music video that "broke the mould for female pop stars“.

Record Business was complimentary of Lennox's "gutsy" vocal delivery and "bluesy wailing" and felt that the song was an effective follow-up to "Love is a Stranger".

[28] Record Mirror thought that the band created a successful hybrid of electronic blues and soul music with "Sweet Dreams".

In 1995, American rapper and singer Swing (aka Richard Silva II) released a dance cover of "Sweet Dreams" featuring the Sweden-based musician and producer Dr. Alban.

Pan-European magazine Music & Media commented, "Nomen est omen; indeed it's a cover of Eurythmics' first hit.

"[80] Alan Jones from Music Week wrote, "From Sweden, Swing featuring Dr. Alban offer a bludgeoning techno version dominated by rap, with occasional reprises of the title line by Birgitta Edoff".

[Nothing] wanted to release our version of Screamin' Jay Hawkins' 'I Put a Spell on You', which was far too dark, sprawling and esoteric, even for some of our own fans.

The music video was directed by American photographer Dean Karr,[95] and was shot near downtown Los Angeles.

It also featured on soundtracks to the films Enron: The Smartest Guys in the Room (2005),[103] Gamer (2009),[104] and A Perfect Day (2015),[105] in movies such as House on Haunted Hill (1999),[106] and Trick 'r Treat (2007),[107] as well as the trailer for Wrath of the Titans (2012),[108] in the pilot episode of The Following,[109] on the BBC drama Luther,[110] and the Nature three-part miniseries "Okavango: River of Dreams".

[112] This video – also directed by Chris Ashbrook – was used as an interlude on her 2009 concert tour The Circus Starring Britney Spears.