The cleavage and polyadenylation specificity factor (CPSF) complex plays a central role in the formation of mRNA 3' ends, being responsible for the recognition of the poly(A) signal sequence, the endonucleolytic cleavage step, and recruitment of poly(A) polymerase. CPSF has been extensively studied for over three decades, and its functions and those of its individual subunits are becoming increasingly well-defined, with much current research focusing on the impact of these proteins on the normal functioning or disease/stress states of cells. In this review, we provide an overview of the general functions of CPSF and its subunits, followed by a discussion of how they exert their functions in a surprisingly diverse variety of biological processes and cellular conditions. These include transcription termination, small RNA processing, and R-loop prevention/resolution, as well as more generally cancer, differentiation/development, and infection/immunity.