Schoenberg's Violin Concerto, Op. 36, was first performed by the Philadelphia Orchestra under the direction of Leopold Stokowski, with Louis Krasner as soloist, on December 6, 1940. It was later recorded by Krasner with the New York Philharmonic under Dimitri Mitropoulos. Interestingly, in a letter dated December 2, 1945, to Krasner, Schoenberg asks which sections the "audience" or "music lovers" may have liked or disliked.

The Violin Concerto was one the first pieces Schoenberg began after immigrating to the United States. It is also one of his first 12-tone compositions since his work on the opera Moses und Aron, after which he began to re-explore the tonal idiom. The concerto was completed on September 23, 1936, after Schoenberg had accepted a professorship at the University of California, Los Angeles, and settled in Brentwood, CA.

In 1937, Schoenberg wrote of the concerto: "[It] is extremely difficult, just as much for the head as for the hands. I am delighted to add another 'unplayable' work to the repertoire. I want the concerto to be difficult and I want the little finger to become longer. I can wait."

Based on a single 12-tone row, the concerto is entirely dodecaphonic. The most notable general characteristics of the concerto are the autonomy of the violin part, the rigorous application of the 12-tone method, and the use of extremely wide intervallic leaps and contrasting registers.

Throughout the first movement, Schoenberg refers to Baroque-era ritornello form in the alternation of solo and orchestra sections. Unfolding slowly, the soloist begins the movement, a gradual layering of instruments occurring until the first orchestral outburst. When the soloist returns, the accompaniment becomes pizzicato strings with sustained woodwind harmonies, supporting new material and row forms. The double- and triple-stop harmonics that follow are a perfect example of the technically difficult passages that make this work infamous. An abrupt tempo change to Vivace marks a new section that is introduced by the orchestra. The soloist and orchestral strings trade figures and partitions of the rows. Schoenberg's cadenza is replete with wide leaps and harmonics, which eventually disappear as the solo violin closes the movement by reiterating its opening notes.

Vertical presentations of row forms are predominant at the beginning of the Andante grazioso second movement. In general, the orchestra plays a much larger role here, often sounding without the soloist and presenting autonomous thematic material. During the first of these orchestral passages, the cellos perform an unusual, repeated melodic third as the rest of the orchestra fills in the row form. The soloist does not become truly dominant until late in the movement, when a lengthy legato melody is accompanied only by strings. A moment before the movement closes, the soloist returns to the opening theme in a lower octave, but it is harmonized differently and trails off after two measures.

Opening with a theme that is motivic in construction, the march-like finale is even more orchestral than the second movement. After the soloist plays the main theme, the orchestra takes over, presenting a great wealth of material. Percussion instruments such as the tambourine, snare drum, cymbal, and triangle, enter near the end of the first orchestral segment, and continue as accompaniment for the ensuing solo passage. After quoting the main theme on a different row, the soloist continues, exploring contrasting registers to an even greater degree than in the first movement. Never again does the orchestra take center stage as it has; the soloist dominates the rest of the proceedings.

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