When cells divide, the genetic material needs to be faithfully segregated. To achieve this, long filaments called microtubules assemble around the chromosomes to pull them to the two new daughter cells. Molecular motors are critical for arranging the microtubules in space and for connecting them into a large dynamic molecular network, called the mitotic spindle. By rebuilding model microtubule networks experimentally from individual components and by using computer simulations, we found out how motors that walk in opposite directions work together to assemble certain parts of the spindle. This work explains how molecular properties of mitotic motors need to be designed in order to enable them to cooperate during the assembly of a higher order network structure that is critical for cell division.