It was an immediate hit in the band's native UK, reaching #12 on the UK Singles Chart on 21 February, and did even better in Australia, hitting #8 to become Duran Duran's first Top 10 hit anywhere in the world.
The song was the first to explicitly acknowledge the fledgling New Romantic fashion movement, with the line "Like some New Romantic looking for the TV sound".
Fairly primitive by the band's later standards, the video features the band (dressed in frilly, floppy New Romantic fashions) playing the song on a white stage tricked out with special effects to look like a platform made of ice or crystal. Interspersed with the performance are shots of the band members alongside the four elements. The video focused closely on the band's faces. The instrumental middle section features friends of the band from the Rum Runner nightclub dancing in their outlandish outfits. At the end of the video, singer Simon Le Bon leaps from the stage, caught in a freeze frame shot above an apparently bottomless abyss.
The video was parodied in the music video for the Dandy Warhols' "You Were The Last High" (which was produced by Nick Rhodes).
Beginning with "Planet Earth", Duran Duran began creating what they called "night versions" for each of their songs: extended remixes that were featured on their 12-inch singles. Back in 1981, the technology to do extended remixes was still quite rudimentary, so the band chose instead to create a new arrangement of the song, loosely based on the version they were playing live at the time. This formed the basis for the "night version".
The "Night Version" of "Planet Earth" appeared in place of the original on some early US releases of the Duran Duran album.
For the 1999 remix album Strange Behaviour, EMI inadvertently unearthed unreleased alternative mixes of both "Planet Earth" and "Hold Back The Rain".
The song was included on the soundtrack to the 1998 film Free Enterprise.
During the first elimination show of Rock Star: Supernova, contestant Matt Hoffer, who was one of the bottom three contestants that week, chose to sing "Planet Earth" for survival. Gilby Clarke derided the song choice, and Hoffer was subsequently cut from the competition for not being "rock" enough. Later, in an interview, Hoffer said that had he known that during the '80s, Duran Duran and Mötley Crüe, Tommy Lee's former band, had allegedly feuded, he would have chosen a different song to perform, as the song choice apparently had offended Lee.