After completing his Piano Concerto (1923 - 24), Stravinsky wanted to further explore the capabilities of the piano as a solo instrument, and so conceived his Concerto for two solo pianos. This rather individual designation was the result of practical considerations: Stravinsky wanted to write a soloistic work that could be performed in cities where no orchestra was in residence, and further, one that he could play with his son Soulima, a skilled musician in his own right.

The composer began work on the Concerto in 1931, but, after completing the first movement, found himself unable to clearly form the sonic picture of two pianos playing simultaneously. To solve this problem, in his words, he "asked the Pleyel company to build me a double piano, in the form of a small box of two tightly wedged triangles." This invention proved useful, and Stravinsky completed the Concerto in 1934 and 1935.

As one might expect, the relationship of the two pianos is more ambiguous than the "concerto" designation implies. The Pleyel piano apparently stimulated Stravinsky's imagination, as he exploits the gamut of possibilities of two pianos working in tandem. The instruments are often used in a solo-and-accompaniment relationship, but at times they work together—or even at odds—in developing material. Both sonata-allegro and ternary forms influence the shape the first movement, which has two sections with two distinct subjects that surround a middle section marked by a Baroque lyricism. The movement's primary character is expressed in its Con moto marking; fast, witty, and delightful. Like the first movement, the Nocturne has a steady pulse, but its main concern is the graceful development of its lovely melody. Still, Stravinsky stretches the performers' capabilities with heavy ornamentation that requires special attention to retain its delicacy. Stravinsky switched the third and fourth movements after they were composed, so the "Quattro variazioni" third movement actually refers to a theme that has not yet been stated. These strongly contrasted variations pave the way for the fourth movement, whose prelude-fugue-prelude-fugue structure recalls the final movement of Beethoven's Piano Sonata No. 31 in A flat major, Op. 110. After a forbidding prelude, the fugue subject—immediately recognizable as the basis for the preceding variations—enters in one piano, posed against a sixteenth-note texture in the other. Further reflecting the influence of Beethoven's sonata, the subject in the second fugue is an inversion of the first fugue's subject.

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