Patterns in the distribution of homoplasy are investigated from theoretical and empirical perspectives. The history of the term "homoplasy" as used by morphologists, evolutionary systematists, cladists, and others is reviewed, especially in relation to its complement, "homology." Homoplasy is defined relative to homology, which is viewed as any similarity shared through an unbroken line of common ancestry. An investigation of levels of homoplasy based on a statistical analysis of 60 published phylogenies reveals a strong dependence of homoplasy on the number of taxa included. This relation is independent of number of characters, type of data, taxonomic rank, or organism, and suggests that large taxa should be the focus of empirical studies of homoplasy. Hence, a phylogenetic analysis of the large genus Astragalus was undertaken using 113 representative species (and varieties) found in North America. Fifty-seven binary and multistate characters were scored and the resulting matrix was subjected to numerical cladistic analysis. Two large sets of equally parsimonious trees were found at 595 and 596 steps. The sets were analyzed using consensus methods, robust clades were discussed in detail, and the phylogenies were compared to previous classifications. Character evolution of a large set of taxonomically important and morphologically varied traits was investigated. Statistical tests were developed to detect patterns of topological clustering of homoplastic character changes in cladograms. The tests use Monte-Carlo computer simulations of four null models of character evolution in an attempt to reject the hypothesis of random homoplastic distributions. For the Astragalus data set only two of 17 characters were significantly clustered, and this is close to random expectation. Another data set from the literature was also tested, and in it no characters were clustered at the 5 percent level. The explanation for these negative findings regarding homoplastic "tendencies" is explored with respect to "scope", "scale", and character "resolution," factors believed to play an important role in the analysis of character evolution.