The ESCRT pathway helps mediate the final abscission step of cytokinesis in mammals and archaea. In mammals, two early acting proteins of the ESCRT pathway, ALIX and TSG101, are recruited to the midbody through direct interactions with the phosphoprotein CEP55. CEP55 resides at the centrosome through most of the cell cycle but then migrates to the midbody at the start of cytokinesis, suggesting that the ESCRT pathway may also have centrosomal links. Here, we have systematically analyzed the requirements for late-acting mammalian ESCRT-III and VPS4 proteins at different stages of mitosis and cell division. We found that depletion of VPS4A, VPS4B, or any of the 11 different human ESCRT-III (CHMP) proteins inhibited abscission. Remarkably, depletion of individual ESCRT-III and VPS4 proteins also altered centrosome and spindle pole numbers, producing multipolar spindles (most ESCRT-III/VPS4 proteins) or monopolar spindles (CHMP2A or CHMP5) and causing defects in chromosome segregation and nuclear morphology. VPS4 proteins concentrated at spindle poles during mitosis and then at midbodies during cytokinesis, implying that these proteins function directly at both sites. We conclude that ESCRT-III/VPS4 proteins function at centrosomes to help regulate their maintenance or proliferation and then at midbodies during abscission, thereby helping ensure the ordered progression through the different stages of cell division.