Active cyclin B1–Cdk1 (cyclin-dependent kinase 1) keeps cells in mitosis, allowing time for spindle microtubules to capture the chromosomes and for incorrect chromosome-spindle attachments to be repaired. Meanwhile, securin, an inhibitor of separase, secures cohesion between sister chromatids, preventing anaphase onset. The spindle checkpoint is a signalling pathway emerging from improperly attached chromosomes that inhibits Cdc20, the mitotic activator of the APC/C (anaphase-promoting complex/cyclosome) ubiquitin ligase. Blocking Cdc20 stabilizes cyclin B1 and securin to delay mitotic exit and anaphase until all chromosomes reach bipolar spindle attachments. Cells entering mitosis in the absence of a functional spindle checkpoint degrade cyclin B1 and securin right after nuclear-envelope breakdown, in prometaphase. Interestingly, two APC/C substrates, cyclin A and Nek2A, are normally degraded at nuclear-envelope breakdown, even when the spindle checkpoint is active. This indicates that the APC/C is activated early in mitosis, whereas cyclin B1 and securin are protected as long as the spindle checkpoint inhibits Cdc20. Remarkably, destruction of cyclin A and Nek2A also depends on Cdc20. The paradox of Cdc20 being both active and inhibited in prometaphase could be explained if cyclin A and Nek2A are either exceptionally efficient Cdc20 substrates, or if they are equipped with ‘stealth’ mechanisms to effectively escape detection by the spindle checkpoint. In the present paper, we discuss recently emerging models for spindle-checkpoint-independent APC/C–Cdc20 activity, which might even have implications for cancer therapy.