The processing of eukaryotic pre-mRNA is an essential step in the synthesis of mRNA in living cells. It involves a coupled cleavage and polyadenylation reaction, in which the pre-mRNA is cleaved at the cleavage site, followed by the processive addition of a poly(A) tail to the upstream pre-mRNA transcript. The poly(A) tail is essential for the stability and export of mature mRNAs from the nucleus, and contributes to translation initiation in the cytoplasm. The Cleavage/Polyadenylation Factor (CPF) is one of the factors responsible for 3’ end processing in yeast cells, and is made up of proteins that facilitate both cleavage and polyadenylation. My dissertation focuses on the mechanisms that regulate 3’ end processing in yeast cells, and how interactions between the proteins that make up CPF play a role in this process. My thesis shows that interactions at the N-terminus of Pap1, a subunit of CPF and the enzyme that catalyzes poly(A) addition, inhibit and stimulate polyadenylation, and I propose a model in which these interactions are controlled by phosphorylation. I also show that Fip1, another subunit of CPF that recruits Pap1 to CPF, has a flexible linker in the middle of the protein, and that removal or replacement of the linker affects the efficiency of polyadenylation. The flexible linker might also facilitate the degradation of Fip1 and suggests another mechanism for the regulation of the polyadenylation step in yeast cells.