Libelluloidea are highly successful dragonflies with unique behavior and life histories. The systematics of Libelluloidea (Odonata: Anisoptera) has historically been in conflict, with little agreement about the number of families that are comprised in this large, heterogeneous group. For my PhD thesis, I have assembled the most comprehensive molecular and morphological libelluloid dataset to date, in an attempt to revise and simplify libelluloid taxonomy, and to answer questions about the evolutionary history of the group. I ran Bayesian and parsimony analyses to recover phylogenetic hypotheses with which I explore the success of Libelluloidea. Divergence estimation, a method by which nodes of a tree are dated, was first explored under different evolutionary models for a subset of libelluloid taxa in order to determine whether treatment of hydrogen-bonded ribosomal nucleotides affected the age of divergence estimates. Using methodology based on these results, I was able to estimate divergence dates and diversification rates for the first large-scale dating analysis of dragonflies. On a smaller scale, I also completed a study of Syncordulia , a vulnerable genus of endemic South African libelluloid dragonflies whose systematics was not yet confirmed. Additional studies of phylogenetic methodology were undertaken in my thesis work for another large and heterogeneous group, the Dictyoptera (Mantodea, Blattodea and Isoptera). In this study, the effect of outgroup selection was determined using a broad, comprehensive taxon set for which we had both molecular and morphological data. These results suggest that the evolution of sociality, on which much of the recent discussion in dictyopteran systematics has focused, cannot be reliably determined when different outgroups recover dramatically conflicting topologies.