Embodiments of the methods and compositions provided herein relate to the selective cleavage of target nucleic acids. Some embodiments include recombinase-mediated selective cleavage of target nucleic acids with single-stranded nucleic acid probes and a recombinase. Some embodiments also include the enrichment of non-target nucleic acids in a sample by selective cleavage of target nucleic acids in the sample, and removal of the cleaved target nucleic acids from the sample.