Background and release
On May 14, 2015, Little Mix officially announced that Black Magic will be the lead single from the third album. Black Magic was scheduled to premiere on May 26th but was later moved forward to May 21st, after the single leaked online on May 20th.
Upon release, "Black Magic" was positively received by contemporary music journalists, who welcomed Little Mix's new '80s influenced sound. Matt Bagwell of the Huffington Post UK called the single "one of the best pop releases of the year", complimenting its "killer chorus" and "trademark call to arms chant", while writing that "Black Magic" is "significantly better" than Britney Spears and Iggy Azalea's single "Pretty Girls", which Little Mix co-wrote.
Ariana Bacle of Entertainment Weekly described the song as "bouncy" and "incredible catchy". Jocelyn Vena of Billboard noted Little Mix's "soaring vocals over a shimmery melody". The Guardian compared the song to the "carefree joy" of Whitney Houston's "I Wanna Dance With Somebody" and Cyndi Lauper's "Girls Just Want to Have Fun", while also comparing the song to those of their debut album DNA (2012).
The song debuted at 25 on the Australian singles chart and two weeks later, it peaked at number 8. The song also charted on both Ultratip Belgian airplay charts, peaking at 4 on the Flanders chart and 37 on the Wallonia chart. On the Israeli television airplay chart, the song peaked at 5. During the midweek chart update for the British singles chart, the song entered at number 1 and stayed there for three consecutive weeks. "Black Magic" had the fourth highest debut of the year in the UK, as well as the biggest preorder sales of 2015. In its first week, the song had combined sales of 113,000, including 1.19 million streams and it became their first UK number one single since their 2012 single "Wings".
In the United States, the song debuted at number 99 on the US Billboard Hot 100 on the week ending August 29, 2015, becoming the group's first entry on the chart since "Wings" (2012). In the second week of it charting on the Billboard Hot 100, it climbed 31 spots to number 68; it achieved a new peak of 67 in its third week on the Hot 100, becoming the group's highest charting US single to date. 
Filming for the music video took place between May 22-23 2015 at the University of Southern California in Los Angeles. It was released May 29, 2015 and was directed by Director X.
The video begins showing the campus, then introduces the band, who are dressed as nerds. They see a super hot boy wave at them, and become excited, but he is actually waving to the popular girl behind them. Sadly, the scene changes to the library, where we see Jade take off her headphones and go search for a book. Suddenly, an old magic book falls on her head, and that night the girls open it. They are given special gifts, like Perrie turns her hair purple, Leigh-Anne has yellow fire powers, Jesy has blue powers, and Jade levitates her glasses. We see the girls made over in beautiful outfits as all the boys stare at their newfound hotness, and they make the mean popular girl fart and burp in front of all the boys. She then runs away, while the scene changes to a nerdy boy being made fun of by 4 popular girls. The band feels bad for him, so they make the girls fall in love with him. We see them walking down the hall as everyone stares, intertwined with a scene of the girls standing back to back as the camera circles them. It then switches to a classroom, where the students are not paying attention to the teacher. The girls use their magic to transform the classroom into a full on dance party, and then even the teacher (along with students) dance on the desks and chairs. They then party their way down the hallways of the school, as the video ends with "By Director X". The video is based off the film The Craft.
Two remixes were released on Little Mix's VEVO channel.