Musical improvisation (also known as musical extemporization) is the creative activity of immediate ("in the moment") musical composition, which combines performance with communication of emotions and instrumental technique as well as spontaneous response to other musicians. Sometimes musical ideas in improvisation are spontaneous, but may be based on chord changes in classical music and many other kinds of music. One definition is a "performance given extempore without planning or preparation". Another definition is to "play or sing (music) extemporaneously, by inventing variations on a melody or creating new melodies, rhythms and harmonies". Encyclopædia Britannica defines it as "the extemporaneous composition or free performance of a musical passage, usually in a manner conforming to certain stylistic norms but unfettered by the prescriptive features of a specific musical text." Improvisation is often done within (or based on) a pre-existing harmonic framework or chord progression. Improvisation is a major part of some types of 20th-century music, such as blues, rock music, jazz, and jazz fusion, in which instrumental performers improvise solos, melody lines and accompaniment parts.

Throughout the eras of the Western art music tradition, including the Medieval, Renaissance, Baroque, Classical, and Romantic periods, improvisation was a valued skill. J. S. Bach, Handel, Mozart, Beethoven, Chopin, Liszt, and many other famous composers and musicians were known especially for their improvisational skills. Improvisation might have played an important role in the monophonic period. The earliest treatises on polyphony, such as the Musica enchiriadis (ninth century), indicate that added parts were improvised for centuries before the first notated examples. However, it was only in the fifteenth century that theorists began making a hard distinction between improvised and written music.

Some classical music forms contained sections for improvisation, such as the cadenza in solo concertos, or the preludes to some keyboard suites by Bach and Handel, which consist of elaborations of a progression of chords, which performers are to use as the basis for their improvisation. Handel and Bach frequently improvised on the harpsichord or pipe organ. In the Baroque era, performers improvised ornaments, and basso continuo keyboard players improvised chord voicings based on figured bass notation. However, in the 20th and early 21st century, as common practice Western art music performance became institutionalized in symphony orchestras, opera houses and ballets, improvisation has played a smaller role. At the same time, some contemporary composers from the 20th and 21st century have increasingly included improvisation in their creative work.

In Indian classical music, improvisation is a core component and an essential criterion of performances. In Indian, Afghan, Pakistani, and Bangladeshi classical music, raga is the "tonal framework for composition and improvisation". The Encyclopædia Britannica defines a raga as "a melodic framework for improvisation and composition".

Although melodic improvisation was an important factor in European music from the earliest times, the first detailed information on improvisation technique appears in ninth-century treatises instructing singers on how to add another melody to a pre-existent liturgical chant, in a style called organum. Throughout the Middle Ages and Renaissance, improvised counterpoint over a cantus firmus (a practice found both in church music and in popular dance music) constituted a part of every musician's education, and is regarded as the most important kind of unwritten music before the Baroque period.

Following the invention of music printing at the beginning of the sixteenth century, there is more detailed documentation of improvisational practice, in the form of published instruction manuals, mainly in Italy. In addition to improvising counterpoint over a cantus firmus, singers and instrumentalists improvised melodies over ostinato chord patterns, made elaborate embellishments of melodic lines, and invented music extemporaneously without any predetermined schemata. Keyboard players likewise performed extempore, freely formed pieces.

The kinds of improvisation practised during the Renaissance—principally either the embellishing of an existing part or the creation of an entirely new part or parts—continued into the early Baroque, though important modifications were introduced. Ornamentation began to be brought more under the control of composers, in some cases by writing out embellishments, and more broadly by introducing symbols or abbreviations for certain ornamental patterns. Two of the earliest important sources for vocal ornamentation of this sort are Giovanni Battista Bovicelli's Regole, passaggi di musica (1594), and the preface to Giulio Caccini's collection, Le nuove musiche (1601/2)

Eighteenth-century manuals make it clear that performers on the flute, oboe, violin, and other melodic instruments were expected not only to ornament previously composed pieces, but also spontaneously to improvise preludes.