Cell division is a highly regulated process requiring the interplay of physical and chemical cues. The cytoskeleton is a central player, serving as energy source for dramatic movements requiring complex mechano-chemistry, as well as acting as a scaffold that facilitates molecular encounters at the right time and place within the cell. We study two cytoskeletal systems, microtubules (MTs) and septin filaments, that play critical roles in mitosis and cytokinesis, respectively. Importantly, their self-assembly and interactions can serve both as input or readout in checkpoint processes that regulate critical and often irreversible steps in cell division progression.