The remarkable antiquity, diversity and ecological significance of arthropods have inspired numerous attempts to resolve their deep phylogenetic history, but the results of two decades of intensive molecular phylogenetics have been mixed. The discovery that terrestrial insects (Hexapoda) are more closely related to aquatic Crustacea than to the terrestrial centipedes and millipedes (Myriapoda) was an early, if exceptional, success. More typically, analyses based on limited samples of taxa and genes have generated results that are inconsistent, weakly supported and highly sensitive to analytical conditions. Here we present strongly supported results from likelihood, Bayesian and parsimony analyses of over 41kilobases of aligned DNA sequence from 62 single-copy nuclear protein-coding genes from 75 arthropod species. These species represent every major arthropod lineage, plus five species of tardigrades and onychophorans as outgroups. Our results strongly support Pancrustacea (Hexapoda plus Crustacea) but also strongly favour the traditional morphology-based Mandibulata (Myriapoda plus Pancrustacea) over the molecule-based Paradoxopoda (Myriapoda plus Chelicerata). In addition to Hexapoda, Pancrustacea includes three major extant lineages of `crustaceans', each spanning a significant range of morphological disparity. These are Oligostraca (ostracods, mystacocarids, branchiurans and pentastomids), Vericrustacea (malacostracans, thecostracans, copepods and branchiopods) and Xenocarida (cephalocarids and remipedes). Finally, within Pancrustacea we identify Xenocarida as the long-sought sister group to the Hexapoda, a result confirming that `crustaceans' are not monophyletic. These results provide a statistically well-supported phylogenetic framework for the largest animal phylum and represent a step towards ending the often-heated, century-long debate on arthropod relationships.