Cohesin, a multi-subunit protein complex, plays important roles in sister chromatid cohesion, DNA replication, chromatin organization, gene expression, transcription regulation, and the recombination or repair of DNA damage. Recently, several studies suggested that the functions of cohesin rely not only on cohesin-related protein–protein interactions, their post-translational modifications or specific DNA modifications, but that some RNA processing factors also play an important role in the regulation of cohesin functions. Therefore, the mutations and changes in the expression of cohesin subunits or alterations in the interactions between cohesin and RNA processing factors have been shown to have an impact on cohesion, the fidelity of chromosome segregation and, ultimately, on genome stability. In this review, we provide an overview of the cohesin complex and its role in chromosome segregation, highlight the causes and consequences of mutations and changes in the expression of cohesin subunits, and discuss the RNA processing factors that participate in the regulation of the processes involved in chromosome segregation. Overall, an understanding of the molecular determinants of the interplay between cohesin and RNA processing factors might help us to better understand the molecular mechanisms ensuring the integrity of the genome.