The field of phylogenetic systematics has benefited greatly from advances in the theory that links the variation among organisms to the evolutionary relationships among the biological lineages to which those organisms belong, and from advances in molecular techniques that allow the rapid and easy access to potentially informative data. Despite the clear benefits (e.g. more exacting methodology, increased participation) that these advances have brought to the field, there is widespread disagreement on the confidence that results produced by different methods of phylogenetic inference should be afforded. The disagreement stems in part from the proliferation of ever more sophisticated methods of phylogenetic inference while our understanding of the evolutionary process that underlies the generation of biological variation lags behind. In addition, such basic issues as the limits of taxonomic sampling and the reconciliation of contradictory hypothesis are often ignored. This dissertation presents three case studies of phylogenetic relationships; each highlighting some of the most important issues that affect the confidence that can be placed on a phylogenetic conclusion. The studies focus on: a group of bony fishes (the Esociformes: Pikes and mudminnows) and two groups of galeomorph sharks (Lamniformes: Mackerel sharks and Triakidae: Houndsharks). The study of the phylogeny of esociform fishes demonstrates the utility of synthesis when conflicting hypothesis are available; especially when data derived from morphological and molecular observations are in conflict. The study of lamniform phylogeny shows the limits of current methods of inference when the evolutionary process under study is heterogeneous as a result of shifting forces shaping the evolution of related lineages and/or uneven patterns of formation and extinction of lineages. Finally, the study of triakid phylogeny illustrates the limits that taxonomic sampling places on the value of the findings of a phylogenetic study when this findings are in conflict with the current classification of the group under examination and it advocates a conservative approach in the proposal of novel phylogenetic hypothesis. The three case studies share in common the use of DNA sequences from the recombination-activating gene-1, therefore an analysis of the characteristics of molecular evolution of that gene also forms part of this work.