Transposases and retroviral integrases promote the movement of DNA segments to new locations within and between genomes. These recombinases function as multimeric protein-DNA complexes. Recent success in solving the crystal structure of a Tn5 transposase--DNA complex provides the first detailed structural information about a member of the transposase/integrase superfamily in its active, DNA-bound state. Here, we summarize the reactions catalyzed by transposases and integrases and review the Tn5 transposase-DNA co-crystal structure. The insights gained from the Tn5 structure and other available structures are considered together with biochemical and genetic data to discuss features that are likely to prove common to the catalytic complexes used by members of this important protein family.