Although most biologists agree that homology must be defined in terms of common ancestry, the details of this definition remain controversial. We review briefly the disagreements concerning the formal definition of homology and the methodology used to establish specific cases of homology. Our principal focus, however, is a third area of disagreement: whether morphological characters can be homologous even if their developmental and genetic bases are not homologous, and whether behavioral characters can be homologous even if their morphological substrates are not homologous. We contend that attempts to reduce behavioral homology to morphological homologies, and morphological homology to genetic and developmental homologies, are misguided and based on a failure to recognize the hierarchical nature of biological organization. Genes, developmental processes, morphological structures, physiological functions and behaviors all constitute different levels of biological organization. These levels are causally interrelated, but there is no one-to-one correspondence between characters at different levels. Furthermore, the causal relationships between characters at different levels may change during the course of evolution. As a result, higher level characters may be homologous, even though some of their constituent lower level characters are not homologous. In support of this assertion, we provide several examples of homologous morphological characters that are based on non-homologous developmental precursors and processes, and of homologous behavioral characters that are based on non-homologous morphological structures. In allowing one to recognize homologies at any level of organization, independently of homologies at other levels, the hierarchical concept of homology also allows one to ask important questions about how evolutionary changes at the various levels of organization are related to one another.