Pteridophytes represent the most poorly understood group of vascular plants from a phylogenetic perspective (Stewart and Rothwell, 1993). The group is probably polyphyletic and includes four extant divisions (following Cronquist et al., 1966): Polypodiophyta (ferns), Psilotophyta (Psilotaceae, or whisk ferns), Lycopodiophyta (lycopods), and Equisetophyta (horsetails). Estimating phylogenetic relationships among these groups, and their relationship to seed plants and to many extinct groups of land plants, remains one of the greatest challenges in plant systematics. In this chapter we review some of the literature bearing on relationships among pteridophytes, focusing on studies of ferns. We also present an exploratory analysis, using nucleotide sequences from three genes and data from 77 morphological characters, to examine the feasibility of a combined approach to inferring pteridophyte phylogeny. We then discuss the problems associated with resolving ancient divergence events and with analyzing large and diverse data sets. We conclude with what we believe to be the most fertile directions for future research on pteridophyte phylogeny.