The cohesin complex facilitates faithful chromosome segregation by pairing the sister chromatids after DNA replication until mitosis. In addition, cohesin contributes to proficient and error-free DNA replication. Replisome progression and establishment of sister chromatid cohesion are intimately intertwined processes. Here, we review how the key factors in DNA replication and cohesion establishment cooperate in unperturbed conditions and during DNA replication stress. We discuss the detailed molecular mechanisms of cohesin recruitment and the entrapment of replicated sister chromatids at the replisome, the subsequent stabilization of sister chromatid cohesion via SMC3 acetylation, as well as the role and regulation of cohesin in the response to DNA replication stress.