Homology is a biological sameness relation that is purported to hold in the face of changes in form, composition, and function. In spite of the centrality and importance of homology, there is no consensus on how we should understand this concept. The two leading views of homology, the genealogical and developmental accounts, have significant shortcomings. We propose a new account, the hierarchical-dependency account of homology, which avoids these shortcomings. Furthermore, our account provides for continuity between special, general, and serial homology.