The assembly of the mitotic spindle and the subsequent segregation of sister chromatids are based on the self-organized action of microtubule filaments, motor proteins, and other microtubule-associated proteins, which constitute the fundamental force-generating elements in the system. Many of the components in the spindle have been identified, but until recently it remained unclear how their collective behaviors resulted in such a robust bipolar structure. Here, we review the current understanding of the physics of the metaphase spindle that is only now starting to emerge.