Starting around the mid-'50s, Lutoslawski began to incorporate unusual sounds and playing techniques into his works. Among these were aleatorics, or chance elements. Lutoslawski first encountered the use of chance in the works of John Cage, and, inspired by that encounter, developed what he called "controlled chance" or "limited aleatoric technique"—the employment of short sections of chance-derived sounds within a larger composition. In a description which also provides an apt metaphor for his Concerto for Cello and Orchestra, in which limited aleatorics are used, Lutoslawski said that the chance element "grants the musicians a touch of self-determination within the otherwise hierarchical, authoritarian organization of conductor and orchestra."

The Cello Concerto was written for and dedicated to Mstislav Rostropovich, for whom Lutoslawski also wrote the Novelette of 1978-1979. Rostropovich took part in the work's premiere, along with the Bournemouth Symphony and conductor Edward Downes, on October 14, 1970. At that time Rostropovich's dissident status within the Soviet Union was well known, and Lutoslawski and members of his family had likewise suffered at the hands of the Soviets. These events must have had some influence, despite Lutoslawski's statements to the contrary, on the dialectic of the Concerto, in which the cellist plays the traditional but innovatively modified role of individual hero in conflict with the orchestra (representing the state or society).

This concerto, in four linked movements, begins with an Introduction, a soliloquy for the cello in which repeated D tones are broken by short, abrupt phrases. After about four minutes, the orchestra finally enters with a loud interruption from the brass instruments. There are four such eruptions in the second movement, Episodes, during most of which the cello carries on a dialogue with members of the orchestra. The slow Cantilena third movement features a lyrical cello solo over a somewhat ominous accompaniment. The intensity builds to near chaos, and in the Finale the cello is, as it were, set upon by the orchestra. After an aggressive back-and-forth between soloist and orchestra and a harsh sustained chord, the cello takes control and leads the way to the resolute ending.

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