Cohesion between replicated chromosomes is essential for chromatin dynamics and equal segregation of duplicated genetic material. In the G1 phase, the ring-shaped cohesin complex is loaded onto duplex DNA, enriching at replication start sites, or “origins”. During the same phase of the cell cycle, and also at the origin sites, two MCM helicases are loaded as symmetric double hexamers around duplex DNA. During the S phase, and through the action of replication factors, cohesin switches from encircling one parental duplex DNA to topologically enclosing the two duplicated DNA filaments, which are known as sister chromatids. Despite its vital importance, the structural mechanism leading to sister chromatid cohesion establishment at the replication fork is mostly elusive. Here we review the current understanding of the molecular interactions between the replication machinery and cohesin, which support sister chromatid cohesion establishment and cohesin function. In particular, we discuss how cryo-EM is shedding light on the mechanisms of DNA replication and cohesin loading processes. We further expound how frontier cryo-EM approaches, combined with biochemistry and single-molecule fluorescence assays, can lead to understanding the molecular basis of sister chromatid cohesion establishment at the replication fork.