"Not Giving Up on Love" is a collaboration between Dutch DJ and record producer Armin van Buuren and English singer Sophie Ellis-Bextor. It was released on 20 August 2010 as the second single from van Buuren's fourth studio album, Mirage, and the fourth single from Ellis-Bextor's fourth studio album, Make a Scene.

The song was written by Australian songwriters Olivia Nervo and Miriam Nervo and Sophie Ellis-Bextor. It premiered on BBC Radio 2's The Dermot O'Leary Show on 11 July 2010 when it was performed in an acoustic version by Sophie Ellis-Bextor. The extended version debuted on Armin van Buuren's radio show A State of Trance on 12 August 2010. On 5 December 2010 it was announced that the song entered the 2010 edition of the Q Top 1000 of all time, compiled by listeners of Dutch radio station Q-Music, on number 545. In the 2011 edition of the Q Top 1000 of all time, the song landed at number 409. The song was nominated at the "2011 International Dance Music Awards" in the category of "Best Commercial Dance Track" and "Best Trance Track", for which it won the award.

"Not Giving Up on Love" is a trance song. It also features euphoric synths and pulsating beats. According to Idolator's Robbie Daw, the opening lyrics to 'Not Giving Up On Love' could almost be describing Sophie’s feelings about her chart fortunes over the past year: "I know you’re feeling restless, like life’s not on your side/It’s weighing heavy on your mind." In the chorus, she sings: "Hold me now, nothing else matters, it’s just the two of us / And if it all falls down, nothing else matters, you know we’re strong enough / I’m not giving up, I’m not giving up on us / I said I’m not giving up, I’m not giving up on love."

The song received positive reviews from most music critics. Jon O'Brien of Allmusic wrote that "on the warm and melancholic multi-layered trance of 'Not Giving Up on Love', she shows her Ibiza soundtrack days aren't as far behind her as first thought." Tom Hocknell of BBC Music commented, "The album’s purple patch continues with Van Buuren’s uplifting Not Giving Up on Love, which sounds like Chicane at the gym." Lewis Corner of Digital Spy awarded it four out of five stars, writing "The result is a club thumper more fabulous and heavy than a Big Fat Gypsy wedding dress." Robert Copsey also of Digital Spy called it "a club-thumping collaboration with superstar DJ Armin van Buuren." Clixie Music called it "typically Sophie, an anthem-driven track."Sputnikmusic's staff wrote that "the song exist only to excite. It's a sleeper club hit just waiting to happen."

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