The anaphase-promoting complex (APC/C) is a multimeric RING E3 ubiquitin ligase that controls chromosome segregation and mitotic exit. Its regulation by coactivator subunits, phosphorylation, the mitotic checkpoint complex and interphase early mitotic inhibitor 1 (Emi1) ensures the correct order and timing of distinct cell-cycle transitions. Here we use cryo-electron microscopy to determine atomic structures of APC/C–coactivator complexes with either Emi1 or a UbcH10–ubiquitin conjugate. These structures define the architecture of all APC/C subunits, the position of the catalytic module and explain how Emi1 mediates inhibition of the two E2s UbcH10 and Ube2S. Definition of Cdh1 interactions with the APC/C indicates how they are antagonized by Cdh1 phosphorylation. The structure of the APC/C with UbcH10–ubiquitin reveals insights into the initiating ubiquitination reaction. Our results provide a quantitative framework for the design of future experiments to investigate APC/C functions in vivo.