The mitotic spindle is the macromolecular machine that segregates chromosomes to two daughter cells during mitosis. The major structural elements of the spindle are microtubule polymers, whose intrinsic polarity and dynamic properties are critical for bipolar spindle organization and function. In most cell types, spindle microtubule nucleation occurs primarily at two centrosomes, which define the spindle poles, but microtubules can also be generated by the chromosomes and within the spindle itself. Many associated factors help organize the spindle, including molecular motors and regulators of microtubule dynamics. The past decade has provided a wealth of information on the molecular players that are critical for spindle assembly as well as a high-resolution view of the intricate movements and dynamics of the spindle microtubules and the chromosomes. In this chapter we provide a historical account of the key observations leading to current models of spindle assembly, as well as an up-to-date status report on this exciting field.