During cell division, the bipolar spindle self-assembles and segregates the genetic material of the cell. For this task, microtubules are arranged in space and time by motor proteins and microtubule bundling proteins. Using in vitro reconstitution experiments with purified proteins and computer simulations, we examine the basic organizational properties of important motors and bundlers required for proper spindle architecture. Using motors acting in metaphase, we uncover the rules determining polar versus nematic microtubule network organization. Using a motor and a bundler acting in anaphase, we show how antiparallel overlaps mimicking the spinde midzone self-organize. These results reveal simple design principles of microtubule organization in the spindle.