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The mitotic spindle is an exquisite microtubule-based molecular machine self-organized for the purpose of capturing and segregating chromosomes during cell division. We examine the active processes at play in assembling and maintaining a functioning spindle. In particular, we focus on the regulation of microtubule length through dynamic instability, spatiotemporal regulation of microtubule nucleation, and active flows of microtubules generated by molecular motors. These core themes of dynamics, nucleation, and transport form the fundamental biophysical building blocks based on which the spindle is built. We then address the emerging idea of intracellular phase separation and protein condensation that has the potential to reshape how we think about these core active processes.

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