In common with most concerti, it has three movements in the pattern quick-slow-quick:
The work was written in 1878 for the violinist and friend of Brahms, Joseph Joachim. Brahms asked Joachim's advice on the writing of the solo violin part. The most familiar cadenzas used in the work are by Joachim, though a number of people have provided alternatives, including Leopold Auer.
The work was premiered by Joachim in Leipzig on January 1, 1879. Various modifications were made between then and the work's publication by Fritz Simrock later in the year. Critical reaction to the work was mixed: the conductor Hans von Bülow said the work was not so much for violin as "against the violin", and the violin virtuoso Pablo de Sarasate refused to play it.