Once all chromosomes are connected to the mitotic spindle (bioriented), anaphase is initiated by the protein ubiquitylation activity of the anaphase-promoting complex/cyclosome (APC/C) and its coactivator Cdc20 (APC/C(Cdc20)). Before chromosome biorientation, anaphase is delayed by a mitotic checkpoint complex (MCC) that inhibits APC/C(Cdc20). We used single-particle electron microscopy to obtain three-dimensional models of human APC/C in various functional states: bound to MCC, to Cdc20, or to neither (apo-APC/C). These experiments revealed that MCC associates with the Cdc20 binding site on APC/C, locks the otherwise flexible APC/C in a "closed" state, and prevents binding and ubiquitylation of a wide range of different APC/C substrates. These observations clarify the structural basis for the inhibition of APC/C by spindle checkpoint proteins.