Homoplasy has been a prominent issue in primate systematics and phylogeny for as long as people have been studying human evolution. In the past, homoplasy, in the form of parallel evolution, was often considered the dominant theme in primate evolution. Today, it receives blame for difficulties in phylogenetic analysis, but is essential in the study of adaptation. This paper reviews the history of study of homoplasy, methods of defining homoplasy, and methodological and biological factors that generate homoplasy. A post hoc definition of homology and homoplasy, based on patterns of character distributions and their congruence or incongruence on a cladogram, is the most consistent method of recognizing these phenomena. Defined this way, homology and homoplasy are mutually exclusive. However, when different levels of analysis are examined, it is seen that homoplasy at one level, such as adult phenotype, often exists simultaneously with homology at a different level, such as developmental process. Thus, in some cases, patterns of homoplasy may point to underlying similarities that reflect the shared heritage of a particular clade. This is an old concept that is being renewed on the strength of recent trends in developmental biology. Factors that influence homoplasy include character definition and a host of biological factors, such as developmental constraints, allometry, and adaptation. These interact with one another to provide explanations of homoplastic patterns. Because of the repetition of events, explanations of homoplastic features are often more reliable than those for homologous features, and serve as effective tests for hypotheses of evolutionary process. In some cases, particular explanations of homoplasy lead to generalizations about the likelihood of homoplasy in a type of structure. The structure may be adaptive or highly epigenetic, or it may belong to an anatomical system considered to be more prone to homoplasy than others. However, our review shows that these generalizations are usually based on theory, and contradictory expectations can be developed under different theoretical models. More rigorous empirical studies are necessary to discover what, if any, generalizations can be made about the likelihood of homoplasy in different types of characters.