In yeast and animals, cyclin B binds and activates the cyclin-dependent kinase ('CDK') CDK1 to drive entry into mitosis. We show that CYCB1, the sole cyclin B in Chlamydomonas, activates the plant-specific CDKB1 rather than the CDK1 ortholog CDKA1, confirming and extending previous results. Time-lapse microscopy shows that CYCB1 is synthesized before each division in the multiple fission cycle, then is rapidly degraded 3-5 minutes before division occurs. CYCB1 degradation is dependent on the anaphase-promoting complex (APC). Like CYCB1, CDKB1 is not synthesized until late G1; however, CDKB1 is not degraded with each division within the multiple fission cycle, but is degraded after all divisions have ceased. The microtubule plus-end-binding protein EB1 labeled with mNeonGreen allowed detection of mitotic events in live cells. The earliest detectable step in mitosis, splitting of polar EB1 signal into two foci, likely associated with future spindle poles, was dependent on CYCB1. CYCB1-GFP localized close to these foci immediately before spindle formation. Spindle breakdown, cleavage furrow formation and accumulation of EB1 in the furrow were dependent on the APC. In interphase, rapidly growing microtubules are marked by 'comets' of EB1; comets are absent in the absence of APC function. Thus CYCB1/CDKB1 and the APC modulate microtubule function and assembly while regulating mitotic progression. Genetic results suggest an independent additional role for the APC in regulating sister chromatid cohesion; this role is likely conserved across eukaryotes.