Proliferating cells need to accurately duplicate and pass their genetic material on to daughter cells. Problems during replication and partition challenge the structural and numerical integrity of chromosomes. Diverse mechanisms, as the DNA replication checkpoint, survey the correct progression of replication and couple it with other cell cycle events to preserve genome integrity. The structural maintenance of chromosomes (SMC) cohesin complex primarily contributes to chromosome duplication by mediating the tethering of newly replicated sister chromatids, thus assisting their equal segregation in mitosis. In addition, cohesin exerts important functions in genome organization, gene expression and DNA repair. These are determined by cohesin’s ability to bring together different DNA segments and, hence, by the fashion and dynamics of its interaction with chromatin. It recently emerged that cohesin contributes to the protection of stalled replication forks through a mechanism requiring its timely mobilization from unreplicated DNA and relocation to nascent strands. This mechanism relies on DNA replication checkpoint-dependent cohesin ubiquitylation and promotes nascent sister chromatid entrapment, likely contributing to preserve stalled replisome-fork architectural integrity. Here we review how cohesin dynamic association to chromatin is controlled through post-translational modifications to dictate its functions during chromosome duplication. We also discuss recent insights on the mechanism that mediates interfacing of replisome components with chromatin-bound cohesin and its contribution to the establishment of sister chromatid cohesion and the protection of stalled replication forks.