Darwin's finches (also known as the Galápagos finches) are a group of about 18 species of passerine birds. They are well known for being a classic example of adaptive radiation and for their remarkable diversity in beak form and function. They are often classified as the subfamily Geospizinae or tribe Geospizini. They belong to the tanager family and are not closely related to the true finches. The closest known relative of the Galápagos finches is the South American dull-coloured grassquit (Asemospiza obscura). They were first collected when the second voyage of the Beagle visited the Galápagos Islands, with Charles Darwin on board as a gentleman naturalist. Apart from the Cocos finch, which is from Cocos Island, the others are found only on the Galápagos Islands.

The term "Darwin's finches" was first applied by Percy Lowe in 1936, and popularised in 1947 by David Lack in his book Darwin's Finches. Lack based his analysis on the large collection of museum specimens collected by the 1905–06 Galápagos expedition of the California Academy of Sciences, to whom Lack dedicated his 1947 book. The birds vary in size from 10 to 20 cm (4 to 8 in) and weigh between 8 and 38 grams (0.3 and 1.3 oz). The smallest are the warbler-finches and the largest is the vegetarian finch. The most important differences between species are in the size and shape of their beaks, which are highly adapted to different food sources. Food availability was different among the islands of the Galapagos and could also change dramatically due to natural events such as droughts. The birds are all dull-coloured. They are thought to have evolved from a single finch species that came to the islands more than a million years ago.

During the survey voyage of HMS Beagle, Darwin was unaware of the significance of the birds of the Galápagos. He had learned how to preserve bird specimens from John Edmonstone while at the University of Edinburgh and had been keen on shooting, but he had no expertise in ornithology and by this stage of the voyage concentrated mainly on geology. In Galápagos he mostly left bird shooting to his servant Syms Covington. Nonetheless, these birds were to play an important part in the inception of Darwin's theory of evolution by natural selection.

On the Galápagos Islands and afterward, Darwin thought in terms of "centres of creation" and rejected ideas concerning the transmutation of species. From Henslow's teaching, he was interested in the geographical distribution of species, particularly links between species on oceanic islands and on nearby continents. On Chatham Island, he recorded that a mockingbird was similar to those he had seen in Chile, and after finding a different one on Charles Island he carefully noted where mockingbirds had been caught. In contrast, he paid little attention to the finches. When examining his specimens on the way to Tahiti, Darwin noted that all of the mockingbirds on Charles Island were of one species, those from Albemarle of another, and those from James and Chatham Islands of a third. As they sailed home about nine months later, this, together with other facts, including what he had heard about Galápagos tortoises, made him wonder about the stability of species.

Following his return from the voyage Darwin presented the finches to the Zoological Society of London on 4 January 1837, along with other mammal and bird specimens that he had collected. The bird specimens, including the finches, were given to John Gould, the famous English ornithologist, for identification. Gould set aside his paying work and at the next meeting, on 10 January, reported that the birds from the Galápagos Islands that Darwin had thought were blackbirds, "gross-beaks" and finches were actually "a series of ground Finches which are so peculiar [as to form] an entirely new group, containing 12 species." This story made the newspapers.

Darwin had been in Cambridge at that time. In early March, he met Gould again and for the first time to get a full report on the findings, including the point that his Galápagos "wren" was another closely allied species of finch. The mockingbirds that Darwin had labelled by island were separate species rather than just varieties. Gould found more species than Darwin had expected, and concluded that 25 of the 26 land birds were new and distinct forms, found nowhere else in the world but closely allied to those found on the South American continent. Darwin now saw that, if the finch species were confined to individual islands, like the mockingbirds, this would help to account for the number of species on the islands, and he sought information from others on the expedition. Specimens had also been collected by Captain Robert FitzRoy, FitzRoy's steward Harry Fuller, and Darwin's servant Covington, who had labelled them by island. From these, Darwin tried to reconstruct the locations from where he had collected his own specimens. The conclusions supported his idea of the transmutation of species.

At the time that he rewrote his diary for publication as Journal and Remarks (later The Voyage of the Beagle), he described Gould's findings on the number of birds, noting that "Although the species are thus peculiar to the archipelago, yet nearly all in their general structure, habits, colour of feathers, and even tone of voice, are strictly American". In the first edition of The Voyage of the Beagle, Darwin said that

It is very remarkable that a nearly perfect gradation of structure in this one group can be traced in the form of the beak, from one exceeding in dimensions that of the largest gros-beak, to another differing but little from that of a warbler.