In eukaryotes, cell proliferation and cell cycle transitions are strictly controlled by the anaphase-promoting complex/cyclosome (APC/C). The APC/C is an E3 ubiquitin ligase that regulates chromatid segregation at the metaphase to anaphase transition, exit from mitosis and the establishment and maintenance of G1. The APC/C’s catalytic activity and substrate specificity are controlled by its interactions with two coactivators, Cdc20 and Cdh1. In contrast to Cdh1, APC/C activation by Cdc20 during mitosis requires hyper-phosphorylation of APC/C subunits by cyclin-dependent kinase (Cdk) and polo kinase. The aim of the first part of this thesis was to understand how mitotic phosphorylation regulates APC/C activity. Using cryo-electron microscopy and biochemical analysis, we found that an auto-inhibitory segment of the Apc1 subunit acts as a molecular switch that in apo unphosphorylated APC/C interacts with a coactivator-binding site (C-box binding site), thereby obstructing engagement of Cdc20. Phosphorylation of the auto-inhibitory segment displaces it from the C-box binding site to relieve APC/C auto-inhibition. Efficient phosphorylation of the auto-inhibitory segment requires the recruitment of the kinase Cdk-cyclin-Cks to a hyper-phosphorylated loop of Apc3. In addition to regulation of APC/C activity by phosphorylation, ordered cell progression is ensured by the ability of the APC/C to target substrate degradation in a defined order. At mitosis onset, degradation of securin and cyclin B1 is inhibited by the spindle assembly checkpoint, exerted by the mitotic checkpoint complex (MCC), whereas both cyclin A2 and Nek2A are not subject to MCC inhibition. The aim of the second part of the thesis was to elucidate the mechanism of how the APC/C achieves its substrate specificity. Our biochemical analysis showed that the resistance of cyclin A2 to MCC inhibition is due to its ABBA motif and the Cdk-associated Cks2 subunit. Furthermore, we found that it is the Cdc20 molecule of the MCC that binds to the ABBA motif to allow for cyclin A2 ubiquitination. Strikingly, mutating all three known degrons (KEN box, D box and ABBA motif) of cyclin A did not affect its ubiquitination by APC/CCdc20. Deletion of a potential novel degron found within residues 60-80 of cyclin A2 impaired cyclin A2 ubiquitination.