Schumann had begun several piano concerti before this one: In 1828, he had begun one in E-flat major; from 1829-31 he worked on one in F major, and in 1839, he wrote one movement of a concerto in D minor. None of these works were completed.
In 1841, Schumann wrote a fantasy for piano and orchestra, his Phantasie. His pianist wife Clara urged him to expand this piece into a full piano concerto. In 1845 he added the intermezzo and finale to make the completed work. It turned out to be the only piano concerto that Schumann completed.
The work premiered in Leipzig on 1 January 1846 with Clara playing the solo part. Ferdinand Hiller, the work's dedicatee, conducted.
The work may have been used as a model by Edvard Grieg in composing his own Piano Concerto, also in A minor. Grieg's concerto, like Schumann's, employs a single powerful orchestral chord at its introduction before the piano's entrance with a similar descending flourish.
Following this concerto, Schumann wrote two other pieces for piano and orchestra: the Introduction and Allegro Appassionato in G major (Op. 92), and the Introduction and Allegro Concertante in D minor (Op. 134).