In biology, homology is similarity in anatomical structures or genes between organisms of different taxa due to shared ancestry, regardless of current functional differences. Evolutionary biology explains homologous structures as retained heredity from a common ancestor after having been subjected to adaptive modifications for different purposes as the result of natural selection.

The term was first applied to biology in a non-evolutionary context by the anatomist Richard Owen in 1843. Homology was later explained by Charles Darwin's theory of evolution in 1859, but had been observed before this from Aristotle's biology onwards, and it was explicitly analysed by Pierre Belon in 1555. A common example of homologous structures is the forelimbs of vertebrates, where the wings of bats and birds, the arms of primates, the front flippers of whales, and the forelegs of four-legged vertebrates like horses and crocodilians are all derived from the same ancestral tetrapod structure.

In developmental biology, organs that developed in the embryo in the same manner and from similar origins, such as from matching primordia in successive segments of the same animal, are serially homologous. Examples include the legs of a centipede, the maxillary and labial palps of an insect, and the spinous processes of successive vertebrae in a vertebrate's backbone.

Sequence homology between protein or DNA sequences is similarly defined in terms of shared ancestry. Two segments of DNA can have shared ancestry because of either a speciation event (orthologs) or a duplication event (paralogs). Homology among proteins or DNA is inferred from their sequence similarity. Significant similarity is strong evidence that two sequences are related by divergent evolution from a common ancestor. Alignments of multiple sequences are used to discover the homologous regions.

Homology remains controversial in animal behaviour, but there is suggestive evidence that, for example, dominance hierarchies are homologous across the primates.

Homology was noticed by Aristotle (c. 350 BC), and was explicitly analysed by Pierre Belon in his 1555 Book of Birds, where he systematically compared the skeletons of birds and humans. The pattern of similarity was interpreted as part of the static great chain of being through the mediaeval and early modern periods: it was not then seen as implying evolutionary change. In the German Naturphilosophie tradition, homology was of special interest as demonstrating unity in nature. In 1790, Goethe stated his foliar theory in his essay "Metamorphosis of Plants", showing that flower parts are derived from leaves. The serial homology of limbs was described late in the 18th century. The French zoologist Étienne Geoffroy Saint-Hilaire showed in 1818 in his theorie d'analogue ("theory of homologues") that structures were shared between fishes, reptiles, birds and mammals. When Geoffroy went further and sought homologies between Georges Cuvier's embranchements, such as vertebrates and molluscs, his claims triggered the 1830 Cuvier–Geoffroy debate. Geoffroy stated the principle of connections, namely that what is important is the relative position of different structures and their connections to each other.

The embryologist Karl Ernst von Baer stated what are now called von Baer's laws in 1828, noting that related animals begin their development as similar embryos and then diverge: thus, animals in the same family are more closely related and diverge later than animals which are only in the same order and have fewer homologies. Von Baer's theory recognises that each taxon (such as a family) has distinctive shared features, and that embryonic development parallels the taxonomic hierarchy: not the same as recapitulation theory. The term "homology" was first used in biology by the anatomist Richard Owen in 1843 when studying the similarities of vertebrate fins and limbs, defining it as the "same organ in different animals under every variety of form and function", and contrasting it with the matching term "analogy" which he used to describe different structures with the same function. Owen codified three main criteria for determining if features were homologous: position, development and composition. In 1859, Charles Darwin explained homologous structures as meaning that the organisms concerned shared a body plan from a common ancestor, and that taxa were branches of a single tree of life.

The word homology, coined in about 1656, is derived from the Greek ὁμόλογος homologos from ὁμός homos 'same' and λόγος logos 'relation'.