The pump organ or reed organ is a type of organ that uses free reeds to generate sound, with air passing over vibrating thin metal strips mounted in a frame. Types include the pressure-based harmonium, the suction reed organ (which employs a vacuum system), and the Indian harmonium. Historical examples include the Kunstharmonium and the American reed organ, while earlier forms include the physharmonica and the seraphine.

More portable than pipe organs, free-reed organs became widespread in smaller churches and private homes during the 19th century, although their volume and tonal range were limited. They generally featured one, or occasionally two, manuals, while pedal-boards were rare. Higher-end pump organs offered a broader range of tones, and models intended for churches or affluent households were often housed in finely crafted cabinets.

Between the 1850s and the 1920s, several million reed organs and melodeons were manufactured in the United States and Canada, with some exported abroad. Major manufacturers included the Cable Piano Company, Estey Organ, and Mason & Hamlin.

In addition to the larger, furniture-sized instruments popular in the West, more compact designs also developed. The portable, hand-pumped Indian harmonium, adapted from Western designs such as the guide-chant in the 19th century, became a central instrument across the Indian subcontinent. Today, the Indian harmonium is widely employed by Sikhs, Hindus, and Muslims for devotional music such as qawwali, ghazal, kirtan, and bhajan. It is also commonly used in Indian classical music and within Western yoga and kirtan subcultures.

During the first half of the 18th century, a free-reed mouth organ called a sheng was brought to Russia. The instrument attracted attention through its use by Johann Wilde. At the time, the free-reed mechanism was unknown in Europe, and the concept quickly spread westward from Russia.

Christian Gottlieb Kratzenstein (1723–1795), a professor of physiology at the University of Copenhagen, is credited with the creation of the first free-reed instrument in the Western world, having won the annual prize in 1780 from the Imperial Academy of St. Petersburg.

The first free-reed organ was built by Abbé Georg Joseph Vogler in Darmstadt after a concept suggested by Kratzenstein. The design of the harmonium, employing free reeds, derives from the earlier regal. A harmonium-like instrument was exhibited by Gabriel-Joseph Grenié (1756–1837) in 1810, which he named the orgue expressif ("expressive organ") due to its capability for greater expression, including crescendos and diminuendos.

Alexandre Debain improved Grenié's design and patented his version under the name harmonium in 1840. There was concurrent development of similar instruments. Jacob Alexandre and his son Édouard introduced the orgue mélodium in 1844. Hector Berlioz discussed it in his Grand traité d'instrumentation et d'orchestration modernes, published in Paris in [1843?] or [1844?], and reprinted in 1856 (critical edition by Peter Bloom, 2003, Bärenreiter, Vol.24). Berlioz also wrote about it in later journals (Bloom, p.472, nn. 1 & 2) and incorporated it into L'enfance du Christ, Part 1, Scene vi, where it was played off-stage. Franz Liszt performed the part during a concert conducted by Berlioz in Weimar on 21 February 1855 (Bloom, p.474, n.3).