Double-strand breaks (DSBs) represent the most severe type of DNA damage since they can lead to genomic rearrangements, events that can initiate and promote tumorigenic processes. DSBs arise from various exogenous agents that induce two single-strand breaks at opposite locations in the DNA double helix. Such two-ended DSBs are repaired in mammalian cells by one of two conceptually different processes, non-homologous end-joining (NHEJ) and homologous recombination (HR). NHEJ has the potential to form rearrangements while HR is believed to be error-free since it uses a homologous template for repair. DSBs can also arise from single-stranded DNA lesions if they lead to replication fork collapse. Such DSBs, however, have only one end and are repaired by HR and not by NHEJ. In fact, the majority of spontaneously arising DSBs are one-ended and HR has likely evolved to repair one-ended DSBs. HR of such DSBs demands the engagement of a second break end that is generated by an approaching replication fork. This HR process can cause rearrangements if a homologous template other than the sister chromatid is used. Thus, both NHEJ and HR have the potential to form rearrangements and the proper choice between them is governed by various factors, including cell cycle phase and genomic location of the lesion. We propose that the specific requirements for repairing one-ended DSBs have shaped HR in a way which makes NHEJ the better choice for the repair of some but not all two-ended DSBs.