To clarify RAD51 interactions controlling homologous recombination, we report here the crystal structure of the full-length RAD51 homolog from Pyrococcus furiosus. The structure reveals how RAD51 proteins assemble into inactive heptameric rings and active DNA-bound filaments matching three-dimensional electron microscopy reconstructions. A polymerization motif (RAD51-PM) tethers individual subunits together to form assemblies. Subunit interactions support an allosteric 'switch' promoting ATPase activity and DNA binding roles for the N-terminal domain helix-hairpin-helix (HhH) motif. Structural and mutational results characterize RAD51 interactions with the breast cancer susceptibility protein BRCA2 in higher eukaryotes. A designed P.furiosus RAD51 mutant binds BRC repeats and forms BRCA2-dependent nuclear foci in human cells in response to gamma-irradiation-induced DNA damage, similar to human RAD51. These results show that BRCA2 repeats mimic the RAD51-PM and imply analogous RAD51 interactions with RAD52 and RAD54. Both BRCA2 and RAD54 may act as antagonists and chaperones for RAD51 filament assembly by coupling RAD51 interface exchanges with DNA binding. Together, these structural and mutational results support an interface exchange hypothesis for coordinated protein interactions in homologous recombination.