DNA transposases use a limited repertoire of structurally and mechanistically distinct nuclease domains to catalyze the DNA strand breaking and rejoining reactions that comprise DNA transposition. Here, we review the mechanisms of the four known types of transposition reactions catalyzed by (1) RNase H-like transposases (also known as DD(E/D) enzymes); (2) HUH single-stranded DNA transposases; (3) serine transposases; and (4) tyrosine transposases. The large body of accumulated biochemical and structural data, particularly for the RNase H-like transposases, has revealed not only the distinguishing features of each transposon family, but also some emerging themes that appear conserved across all families. The more-recently characterized single-stranded DNA transposases provide insight into how an ancient HUH domain fold has been adapted for transposition to accomplish excision and then site-specific integration. The serine and tyrosine transposases are structurally and mechanistically related to their cousins, the serine and tyrosine site-specific recombinases, but have to date been less intensively studied. These types of enzymes are particularly intriguing as in the context of site-specific recombination they require strict homology between recombining sites, yet for transposition can catalyze the joining of transposon ends to form an excised circle and then integration into a genomic site with much relaxed sequence specificity.In this chapter, we provide an overview of the fundamental concepts of DNA transposition mechanisms. Our aim is to emphasize basic themes and, in this effort, we will focus on specific illustrative cases rather than attempt an exhaustive review of the literature. We hope that the selected references will point the curious reader towards the landmark studies in the field as well as some of the most exciting recent results. We also direct the reader to other recent reviews (1-3).DNA transposases are enyzmes that move discrete segments of DNA called transposons from one location in the genome (often called the donor site) to a new site without using RNA intermediates. DNA transposases are usually encoded by the mobile element itself (in which case they are "autonomous" transposons). However, some transposons are missing a self-encoded transposase yet have ends that can be recognized by a transposase encoded somewhere else in the genome, and thus are "non-autonomous" (Siguier et al., this volume). Although logic suggests that all DNA transposons are moved by transposases, the term was originally reserved for those enzymes that do not require significant regions of homology between any part of the transposon and the sites to which they are moved, the so-called target (or insertion or integration) sites. As biology is not always neat and tidy, transposases can exhibit a spectrum of homology requirements and vagaries of terminology have arisen such that certain transposases are sometimes referred to as "resolvases" or by the generic term "recombinases".From a mechanistic perspective, t...