Island biotas have become paradigms for illustrating many evolutionary processes. The fauna of the Galapagos Islands includes several taxa that have been focal points for evolutionary studies. Perhaps their most famous inhabitants, Darwin’s finches, represent a go-to icon when thinking about how species originate and adapt to the environment. However, unlike other adaptive radiations, past morphological and molecular studies of Darwin’s finches have yielded inconsistent hypotheses of species limits and phylogenetic relationships. Expecting that idiosyncrasies of prior data and analytic methods explained different proposed classifications, we were surprised to observe that three new phylogenetic hypotheses derived mostly from the same genomics data were topologically inconsistent. We found that the differences between some of these genomics trees were as great as one would expect between two random trees with the same number of taxa. Thus, the phylogeny of Darwin’s finches remains unresolved, as it has for more than a century. A component of phylogenetic uncertainty comes from unclear species limits, under any species concept, in the ground finches (Geospiza) and tree finches (Camarhynchus). We suggest that past authors should have tested the species limits of Lack, rather than uncritically accepting them. In fact, the impressive amount of genomics data do not provide unambiguous hypotheses of the number of species of Geospiza or Camarhynchus, although they imply greater species diversity than Lack’s taxonomy. We suggest that insufficient sampling of species populations across islands (35.6% for morphometrics and 20.4% for genomics) prevents accurate diagnoses of species limits. However, it is unknown whether samples from a greater number of islands might result in bridging differences between species, or reveal many new ones. We conclude that attempts to interpret patterns of variation among the finches under standard evolutionary paradigms have obscured some major messages, most specifically the ongoing reciprocal interactions between geographic isolation and lineage divergence, and dispersal and gene flow caused by the volatile ecological conditions in the islands. Although the finches provide textbook examples of natural selection, better understanding of species limits and a robust phylogenetic hypothesis are required to corroborate past hypotheses of speciation and adaptive radiation in the finches of the Galapagos.