Mitotic progression is orchestrated by morphological and mechanical changes promoted by the coordinated activities of the microtubule (MT) cytoskeleton, the actin cytoskeleton and the plasma membrane (PM). MTs assemble the mitotic spindle, which assists sister chromatid separation, and contact the rigid and tensile actomyosin cortex rounded-up underneath the PM. Here, we highlight the dynamic crosstalk between MTs, actin and cell membranes during mitosis, and discuss the molecular connections between them. We also summarize recent views on how MT traction forces, the actomyosin cortex and membrane trafficking contribute to spindle positioning in isolated cells in culture and in epithelial sheets. Finally, we describe the emerging role of membrane trafficking in synchronizing actomyosin tension and cell shape changes with cell–substrate adhesion, cell–cell contacts and extracellular signalling events regulating proliferation.