Jazz improvisation is the spontaneous invention of melodic solo lines or accompaniment parts in a performance of jazz music. It is one of the defining elements of jazz. Improvisation is composing on the spot, when a singer or instrumentalist invents melodies and lines over a chord progression played by rhythm section instruments (piano, guitar, double bass) and accompanied by drums. Although blues, rock, and other genres use improvisation, it is done over relatively simple chord progressions which often remain in one key (or closely related keys using the circle of fifths, such as a song in C Major modulating to G Major).

Jazz improvisation is distinguished from this approach by chordal complexity, often with one or more chord changes per bar, altered chords, extended chords, tritone substitution, unusual chords (e.g., augmented chords), and extensive use of ii–V–I progression, all of which typically move through multiple keys within a single song. However, since the release of Kind of Blue by Miles Davis, jazz improvisation has come to include modal harmony and improvisation over static key centers, while the emergence of free jazz has led to a variety of types of improvisation, such as "free blowing", in which soloists improvise freely and ignore the chord changes.

When soloing, a performer (instrumentalist or singer) creates a new melodic line to fit a song's chord progression. During a solo, the performer who is playing the solo is the main focus of the audience's attention. The other members of the group usually accompany the solo, except for some drum solos or bass solos in which the entire band may stop while the drummer or bassist performs.

When a singer improvises a new melody over chord changes, it is called scat singing. When singers are scat-singing, they typically use made-up syllables ("doo-bie-doo-ba"), rather than use the lyrics of the song. Soloing is often associated with instrumental or vocal virtuosity; while many artists do use advanced techniques in their solos, this is not always done. For example, some 1940s and 1950s-era bass solos consist of the bassist playing a walking bassline.

There are a number of approaches to improvising jazz solos. During the swing era, performers improvised solos by ear by using riffs and variations on the tune's melody. During the bebop era in the 1940s, jazz composers began writing more complex chord progressions. Saxophone player Charlie Parker began soloing using the scales and arpeggios associated with the chords in the chord progression.

In jazz, when one instrumentalist or singer is doing a solo, the other ensemble members play accompaniment parts. While fully written-out accompaniment parts are used in large jazz ensembles, such as big bands, in small groups (e.g., jazz quartet, piano trio, organ trio, etc.), the rhythm section members typically improvise their accompaniment parts, an activity called comping. In jazz, the instruments in the rhythm section depend on the type of group, but they usually include a bass instrument (double bass, electric bass), one or more instruments capable of playing chords (e.g., piano, electric guitar) and drum kit. Some ensembles may use different instruments in these roles. For example, a 1920s-style Dixieland jazz band may use tuba as a bass instrument and banjo as the chordal instrument. A 1980s-era jazz-rock fusion band may use synth bass for the bassline and a synthesizer for chords. Some bands add one or more percussionists.

In small groups, the rhythm section members typically improvise their accompaniment parts. Bass instrument players improvise a bassline using the chord progression of the key as a guide. Common styles of bass comping parts include a walking bassline for 1920s-1950s jazz; rock-style ostinato riffs for jazz-rock fusion; and Latin basslines for Latin jazz. Improvised basslines typically outline the harmony of each chord by playing the root, third, fifth and seventh of each chord, and playing any other notes that the composer has requested in the chord (e.g., if the chord chart indicates a sixth chord on the tonic in C Major, the bassist might include the sixth degree of the C Major scale, an "A" note, in their bassline).

The chordal instrument players improvise chords based on the chord progression. Chordal instrument players use jazz chord voicings that are different from those used in popular music and classical music from the common practice period. For example, if a pop musician or one from the Baroque music era (ca. 1600-1750) were asked to play a dominant seventh chord in the key of C Major, they would probably play a root position chord named G7 (or "G dominant seventh"), which consists of the notes G, B, D and F, which are the root, third, fifth and flat seventh of the G chord. A post-Bebop era jazz player who was asked to play a dominant seventh chord in the key of C Major might play an altered dominant chord built on G. An altered dominant contains flattened or sharpened "extensions" in addition to the basic elements of the chord. As well, in jazz, chordal musicians often omit the root, as this role is given to the bass player. The fifth of the chord is often omitted as well, if it is a perfect fifth above the root (as is the case in regular major chords and minor chords).