At the onset of division, the cell forms a spindle, a precise self-constructed micromachine composed of microtubules and the associated proteins, which divides the chromosomes between the two nascent daughter cells. The spindle arises from self-organization of microtubules and chromosomes, whose different types of motion help them explore the space and eventually approach and interact with each other. Once the interactions between the chromosomes and the microtubules have been established, the chromosomes are moved to the equatorial plane of the spindle and ultimately toward the opposite spindle poles. These transport processes rely on directed forces that are precisely regulated in space and time. In this review, we discuss how microtubule dynamics and their rotational movement drive spindle self-organization, as well as how the forces acting in the spindle are generated, balanced, and regulated.