The execution of recombinational pathways during the repair of certain DNA lesions or in the meiotic program is associated to the formation of joint molecules that physically hold chromosomes together. These structures must be disengaged prior to the onset of chromosome segregation. Failure in the resolution of these linkages can lead to chromosome breakage and nondisjunction events that can alter the normal distribution of the genomic material to the progeny. To avoid this situation, cells have developed an arsenal of molecular complexes involving helicases, resolvases, and dissolvases that recognize and eliminate chromosome links. The correct orchestration of these enzymes promotes the timely removal of chromosomal connections ensuring the efficient segregation of the genome during cell division. In this review, we focus on the role of different DNA processing enzymes that collaborate in removing the linkages generated during the activation of the homologous recombination machinery as a consequence of the appearance of DNA breaks during the mitotic and meiotic programs. We will also discuss about the temporal regulation of these factors along the cell cycle, the consequences of their loss of function, and their specific role in the removal of chromosomal links to ensure the accurate segregation of the genomic material during cell division.