This chapter is a critical review of the problems presented by our current knowledge of the early fossil record of tetrapods. This record is marked by two major features. The first is a significant absence of preserved fossils between the Upper Devonian and the end of the Lower Carboniferous: Romer's Gap. The second is that the numerous lineages that appear at the end of the Lower Carboniferous are diverse and distinct from one another and do not present features that permit the confident assignment of relationships either to the Devonian taxa or among the several lineages themselves. Furthermore, convergence in anatomical characteristics is common. Phylogenetic systematics, also termed cladistics, currently plays a major role in the analysis of relationships and patterns of evolution among vertebrates. This mode of analysis does not consider the relative incompleteness of the fossil record, the relative frequency of convergence in the evolution of character changes that may occur independently in more than a single major lineage, development, or body function, none of which can be readily categorized with standard data matrices. These problems in the available data and its mode of analysis are discussed in the context of the early stages in the evolution of terrestrial vertebrates.