Structural models of site-specific recombinases from the lambda integrase family of enzymes have in the last four years provided an important new perspective on the three-dimensional nature of the recombination pathway. Members of this family, which include the bacteriophage P1 Cre recombinase, bacteriophage lambda integrase, the yeast Flp recombinase, and the bacterial XerCD recombinases, exchange strands between DNA substrates in a stepwise process. One pair of strands is exchanged to form a Holliday junction intermediate, and the second pair of strands is exchanged during resolution of the junction to products. Crystal structures of reaction intermediates in the Cre-loxP site-specific recombination system, together with recent biochemical studies in the field, support a "strand swapping" model for recombination that does not require branch migration of the Holliday junction intermediate in order to test homology between recombining sites.