"I've Got You Under My Skin" is a song written by American composer Cole Porter in 1936. It was introduced that year in the Eleanor Powell musical film Born to Dance in which it was performed by Virginia Bruce. It was nominated for the Academy Award for Best Original Song that year but lost out to The Way You Look Tonight. Popular recordings in 1936 were by Ray Noble and his Orchestra (vocal by Al Bowlly) and by Hal Kemp and his Orchestra (vocal by Skinnay Ennis).

Sinatra first sang the song in 1946 on his weekly radio show, as the second part of a medley with "Easy to Love". He recorded a studio version of the song with Nelson Riddle orchestral arrangement, accompanied by Irv Cottler on drums and slide trombone solo by Milt Bernhart at Capitol's Melrose Avenue studios for his 1956 album Songs for Swingin' Lovers! Riddle was a fan of Maurice Ravel and said that this arrangement was inspired by the Boléro. Sinatra aficionados usually rank this as one of his finest collaborations with Riddle's orchestra.

Sinatra re-recorded "I've Got You Under My Skin" for the album Sinatra's Sinatra (1963), an album of re-recordings of his favourites. This time the trombone solo was by Dick Nash because Bernhart was unavailable. Sinatra usually included "I've Got You Under My Skin" in his concerts—a tradition carried on by his son, Frank Sinatra Jr.