Originally released in 1993 under the band name State of Grace, it was re-released in March 1995 as the first single from their only album, If I Could Fly (1996).

Considine from The Baltimore Sun remarked in his review of If I Could Fly, "But rather than try to make the listener dance, as so many divas do, Grace would rather entice us — and there's something wonderfully inviting about that.

"[6] Larry Flick from Billboard wrote, "Grace has it all—a highly videogenic image, an angelic voice, and the ability to write material that deftly straddles commercial viability and underground hipness.

She has already wooed punters in her native U.K. with this silky slice of trance/disco, and early reaction from tastemaking radio-programmers hints that even greater stateside success is on the horizon.

[19] In 2016, Attitude ranked it number five on their list of "The Top 10 Dance Tunes of the '90s", writing, "There are some beautiful '90s tracks that got lost in the 'novelty' of the '90s, and this is one of them.

"[20] In 2018, Mixmag ranked it as one of "The 15 best mid-90s trance tracks", adding, "Dominique Wilkins' soaring vocals steal the show and she delivers one of dance's most recognisable earworms on the hook in a storm of sonic, melody-driven madness.

"[21] In 2020, RedBull.com ranked it number five in their "10 Underrated Dance Songs from the 1990s That Still Sound Amazing", writing, "Sometimes, you just want a big hands-in-the-air singalong.

[23] In 2022, Classic Pop ranked "Not Over Yet" number 21 in their list of the top 40 dance tracks from the 90's, naming it a "90s chart trance cornerstone".

[2] In 1999, "Not Over Yet" was re-released by Planet Perfecto, a supergroup consisting of Paul Oakenfold, Ian Masterson and Jake Williams which featured re-recorded vocals and new mixes.

A remixed version with new vocals (by Ryan Tedder of OneRepublic), only featuring the words "not over yet" from the original appeared on Oakenfold's 2006 album A Lively Mind as "Not Over".

The song was sampled by UK live drum act The Stickmen Project on their 2023 track "Not Over Yet" (Spinnin' Records).

"Not Over Yet" was covered by British band Klaxons as "It's Not Over Yet" and released as the fifth official single from their debut album, Myths of the Near Future (2007).