Elgar dedicated the piece to "my friends pictured within", each variation being an affectionate portrayal of one of his circle of close acquaintances. See Musical cryptogram. The people portrayed in the variations include Elgar's wife Alice, Augustus J. Jaeger and Elgar himself. The enigma is the hidden theme, which has been the subject of much speculation. Various musicians have proposed theories for what melody it could be, although Elgar did not say that that his "theme" was a melody. The enigma could be something else, such as a symbol or a literary theme. Elgar accepted none of the solutions proposed in his lifetime, and took the secret with him to the grave.
After its 1899 London premiere, the piece achieved popularity and was performed internationally. It has been recorded over 60 times.