This album yielded several US hit singles, the most successful of which was the "Missing You" (#10 Pop, #1 R&B, #4 AC). "Missing You" was produced by Lionel Richie and was a tribute to late soul singer Marvin Gaye, Ross and Richie's former Motown Records label-mate. Other singles included the Daryl Hall and Arthur Baker-produced "Swept Away" (#19 Pop, #3 R&B) and the Julio Iglesias duet, "All of You" (#19 Pop, #38 R&B, #2 AC). All three of these singles were accompanied by popular music videos. The album also included the #13 R&B single, "Telephone", produced by Bernard Edwards.
Swept Away was certified Gold by the end of 1984. It peaked at #26 on Billboard Pop albums chart, making this her last album to reach the Top 40 until I Love You in 2007. The record had sold close to 900,000 copies at the time of its deletion. The album also made the top ten in the Netherlands, Sweden and Norway.