Hybridization is increasingly recognized as a creative evolutionary force contributing to adaptation and speciation. Homoploid hybrid speciation—the process in which hybridization results in a stable, fertile, and reproductively isolated hybrid lineage where there is no change in ploidy—has been documented in several taxa. Hybridization can directly contribute to reproductive isolation or reinforce it at a later stage. Alternatively, hybridization might not be related to the evolution of reproductive isolation. To account for these different scenarios, I propose to discriminate between two types of hybrid speciation: type I where reproductive isolation is a direct consequence of hybridization and type II where it is the by‐product of other processes. I illustrate the applicability of this classification scheme with avian examples. To my knowledge, seven hybrid bird species have been proposed: Italian sparrow, Audubon's warbler, Genovesa mockingbird, Hawaiian duck, red‐breasted goose, golden‐crowned manakin, and a recent lineage of Darwin's finches on the island of Daphne Major (“Big Bird”). All studies provide convincing evidence for hybridization, but do not always confidently discriminate between scenarios of hybrid speciation and recurrent introgressive hybridization. The build‐up of reproductive isolation between the hybrid species and their parental taxa is mainly driven by premating isolation mechanisms and comparable to classical speciation events. One hybrid species can be classified as type I (“Big Bird”) while three species constitute type II hybrid species (Italian sparrow, Audubon's warbler, and golden‐crowned manakin). The diversity in hybrid bird species across a range of divergence times also provides an excellent opportunity to study the evolution of hybrid genomes in terms of genome stabilization and adaptation.