The lagomorphs (from Ancient Greek λαγώς lagós 'hare' and μορφή morphḗ 'form') are the members of the taxonomic order Lagomorpha, of which there are two living families: the Leporidae (rabbits and hares) and the Ochotonidae (pikas). There are 110 recent species of lagomorph, of which 109 species in twelve genera are extant, including ten genera of rabbits (42 species), one genus of hare (33 species), and one genus of pika (34 species).

The name "lagomorph" is derived from two Ancient Greek terms: lagos (λαγώς) 'hare' and morphē (μορφή) 'form'. Together, they describe an animal that is "hare shaped". The title is first attested to in the 19th century. It was coined by the German naturalist Johann Friedrich von Brandt in 1855, who called for a reorganization of the subdivision of rodents containing the rabbits, hares, and pikas, but the term "Lagomorpha" was only a suborder and was not formally described as an order until American palaeontologist James W. Gidley described it as such in 1912.

Other names used for this order, now considered synonymous, include: Duplicidentata (Illiger, 1811); Leporini and Leporinorum (Fischer, 1917); Leporida (Averianov, 1999); Neolagomorpha (Averianov, 1999); Ochotonida (Averianov, 1999); and Palarodentia (Haeckel, 1895; Lilian, 2016). The lagomorphs were first described as a group distinct from the rest of the rodents, as they were first classified, in 1811 by Johann Karl Wilhelm Illiger when he erected Duplicidentata. At the time, the rabbit, pikas, and hares were contained in only two genera, Lepus and Lagomys (the hares and the pikas), and it was seen as necessary to further distinguish these animals from rodents based on their teeth, specifically the lagomorphs' four upper incisors. Naturalists would apply various names to this grouping through the following decades, with one of these names being Leporidae, which would later be used to describe just the hares and rabbits. Johann Friedrich von Brandt created the name Lagomorpha in 1855, and this name was solidified as an order in 1912.

The evolutionary history of the lagomorphs is still not well understood. In the late 20th century, it was generally agreed that Eurymylus, which lived in eastern Asia and dates back to the late Paleocene or early Eocene, was an ancestor of the lagomorphs. Examination of the fossil evidence in the 21st century suggested that the lagomorphs may have instead descended from mimotonids, mammals present in Asia during the Paleogene with similar body size and dental structure to early European rabbits such as Megalagus turgidus, while Eurymylus was more closely related to rodents (although not a direct ancestor). The leporids first appeared in the late Eocene and rapidly spread throughout the Northern Hemisphere; they show a trend towards increasingly long hind limbs as the modern leaping gait developed. The pikas appeared somewhat later in the Oligocene of eastern Asia.

Lagomorphs were certainly more diverse in the past than in the present, with around 75 genera and over 230 species represented in the fossil record and many more species in a single biome. This is evidence that lagomorph lineages are declining.

A 2008 study suggests an Indian origin for the order, having possibly evolved in isolation when India was an island continent in the Paleocene.

Lagomorphs are similar to other mammals in that they all have hair, four limbs (i.e., they are tetrapods), and mammary glands and are endotherms. Lagomorphs possess a moderately fused postorbital process to the cranium, unlike other small mammals. They differ in that they have a mixture of "basal" and "derived" physical traits.

Lagomorphs and rodents form the clade or grandorder Glires. Despite the evolutionary relationship between lagomorphs and rodents, the two orders have some major differences.