Chromosomal translocations and genomic instability are universal hallmarks of tumor cells. While the molecular mechanisms leading to the formation of translocations are rapidly being elucidated, a cell biological understanding of how chromosomes undergo translocations in the context of the cell nucleus in vivo is largely lacking. The recent realization that genomes are non-randomly arranged within the nuclear space has profound consequences for mechanisms of chromosome translocations. We review here the emerging principles of spatial genome organization and discuss the implications of non-random spatial genome organization for the genesis and specificity of cancerous chromosomal translocations.