Arthropods are the most species-rich group of animals, and as such they exhibit an amazing diversity of morphological, behavioral, and ecological adaptations. Because of this diversity, the evolutionary history of this group has been, and still is notoriously difficult to determine because considerations of different traits invariably support alternative evolutionary relationships. Their nervous systems provide an invaluable set of characters for systematic inferences about the origins and evolutionary trajectories of Arthropoda. This is because nervous systems are ubiquitous and contain a wealth of structures from which to infer shared ancestry. Considerations of ancestral arthropod relationships have further provided insights into how arthropod nervous systems have maintained some traits through evolutionary time and how others have been modified or acquired as novelties. This dissertation explores the evolution of arthropod brains within an interdisciplinary framework, utilizing comparative neuroanatomical, neural cladistic, and molecular phylogenetic analyses to support novel hypotheses of nervous system evolution in arthropods. The field of neurophylogenetics relies on the characterization of shared derived neural traits to infer ancestry amongst taxa. The first portion of this work describes highly conserved neural elements from the lamina, or first optic neuropil, of several crustaceans. This study is followed by a neural cladistic study that infers evolutionary relationships amongst major arthropod groups based solely on neural traits. The results of this study are then compared to those from a large-scale molecular phylogenomic analysis of hundreds of conserved orthologous genes. Results from neural cladistic and molecular phylogenetics suggest several species whose neuroanatomical characterization would provide support for novel evolutionary hypotheses. The last portion of this dissertation details a comparative neuroanatomical study on one such diagnostic taxa, the copepod Tigriopus californicus. Two principles of arthropod nervous system organization and evolution are repeatedly supported with this approach: 1) many complex neural structures shared amongst arthropod groups have been inherited from ancient common ancestors, suggesting that the neural arrangements seen today have been carried over from antiquity; and 2) these same complex attributes are absent in numerous late-diverging lineages, supporting the hypothesis that secondary simplification of nervous systems is a common property of arthropods.