The Spanish-language version, "Y Caigo Un Poco Mas", was also released in 1994, on her album Alma de Barro.

In 1996, the song was covered by Canadian singer Celine Dion, and released as the first single from her 1996 album, Falling into You.

Rick Nowels offered the song to Belinda Carlisle for her album A Woman & a Man.

Carlisle recorded a demo, which Nowels later played for Dion, but the song was rejected by her then-manager, Miles Copeland III.

[3]AllMusic senior editor Stephen Thomas Erlewine marked "Falling into You" as one of the standouts on the album.

[5] Caroline Sullivan from The Guardian said in her review of the album, "Only the autumnal Falling Into You and the hint-of-reggae (really) Make You Happy diverge from the mainstream".

[6] Pan-European magazine Music & Media described it as "a slow lullaby of a ballad, punctuated in the intro and outtro by Spanish guitars, martial sounding drum rolls and a Careless Whisper type sax riff.

"[7] A reviewer from Music Week rated it five out of five, adding, "Less is more on this restrained, angelically sung ballad, quite possibly Dion's most beautiful yet.

"[8] Christopher Smith from TalkAboutPopMusic noted that it is "sultry and schmoozy with only a hint of saxophone in the latter stages that add to the mood and sexiness of this down-tempo pop-ballad.

"[9] The music video for the song was directed by British director Nigel Dick between 18–19 January 1996 in Gorbio, France and released in February 1996.

Then a fire artist comes on stage and Dion assists him with handing him torchs, while he performs.

[10] In March 2021, the video has been remastered in HD quality to celebrate the 25th anniversary of the album's release.