The development of cancer is associated with alterations to the physiology of the cell caused by multiple changes in its genome. A frequent genomic event in cancer is chromosome translocation, an exchange of large DNA fragments between two non-homologous chromosomes that in many cases leads to the creation of new fusion genes. Chromosome translocations are key events in the initiation or progression of many neoplastic processes. The difficulty in generating specific chromosome translocations in the laboratory has meant that researchers have lacked appropriate cellular models in which to investigate the effect of these key cancer markers. Different genome-engineering strategies used to induce defined chromosome translocations have met with varying success. Recently, the use of the RGEN technology (RNA-guided endonuclease), also known as the CRISPR/Cas9 system, has demonstrated as proof-of-principle that it is possible to engineer cells to undergo these specific chromosomal translocations with high efficiency. Using this advance, it is now possible to easily and accurately generate cell models harboring the same alterations that define tumor cells from patients, allowing researchers to experimentally recapitulate the genomic alterations needed to transform a healthy cell. In this review, we summarize the different methods used to mimic cancer-related chromosomal translocations and highlight the advantages of RGEN technology for improving the generation of models for the study of cancer. These advances will in time lead to the development of better therapeutic approaches to the treatment of cancer.