With the exception of the fourth concerto (a work for the left hand commissioned by Paul Wittgenstein), Prokofiev's five piano concertos were composed as vehicles for his own prodigious keyboard talents. The composer had begun writing his third concerto in 1916 but much work remained in March of 1918, when he traveled to America via Tokyo, arriving in San Francisco but soon hopping a train for New York when the California authorities took him for a Bolshevik spy.

Prokofiev had previously made the acquaintance of Cyrus McCormick, president of the International Harvester Company. McCormick liked modern music and Prokofiev liked machines, so the industrialist told the composer to look him up if he ever found himself in Chicago. On this basis Prokofiev traveled from New York to the Windy City, where the Chicago Symphony played the Scythian Suite and the Lyric Opera agreed to mount his opera The Love for the Three Oranges. In the summer of 1921 Prokofiev found time to complete his third piano concerto, and he gave the premiere with the Chicago Symphony the following December to rave reviews.

An inveterate recycler, Prokofiev had been collecting themes for the work since 1913, when he jotted down the march tune that would form the basis of the second movement's theme and variations. By the time he sat down to complete the work in 1921, he had before him all but two of the many melodic ideas heard in the concerto.

The first movement opens with a languid clarinet solo, magically blossoming to reveal two clarinets and then all of the woodwinds, before the piano launches into excited sixteenth-note passage that propels the rest of the movement. After the central theme-and-variations movement comes a finale cast largely in 3/4, full of sharp humor and virtuoso passages for the piano. Although all five of Prokofiev's concertos are wonderful in their own right, it is the third that has found a central place in the repertoire.