In bacteria, two categories of specialised recombination promote a variety of DNA rearrangements. Transposition is the process by which genetic elements move between different locations of the genome, whereas site-specific recombination is a reaction in which DNA strands are broken and exchanged at precise positions of two target DNA loci to achieve determined biological function. Both types of recombination are represented by diverse genetic systems which generally encode their own recombination enzymes. These enzymes, generically called transposases and site-specific recombinases, can be grouped into several families on the basis of amino acid sequence similarities, which, in some cases, are limited to a signature of a few residues involved in catalysis. The well characterised site-specific recombinases are found to belong to two distinct groups whereas the transposases form a large super-family of enzymes encompassing recombinases from both prokaryotes and eukaryotes. In spite of important differences in the catalytic mechanisms used by these three classes of enzymes to cut and rejoin DNA molecules, similar strategies are used to coordinate the biochemical steps of the recombination reaction and to control its outcome. This review summarises our current understanding of transposition and site-specific recombination, attempting to illustrate how relatively conserved DNA cut-and-paste mechanisms can be used to bring about a variety of complex DNA rearrangements.