Microtubules and other proteins self-organize into complex dynamic structures such as the mitotic spindle, which separates the chromosomes during cell division. Much is known about the individual molecular players involved in assembly and positioning of the mitotic spindle, but how they act together to generate the often unexpected behavior of the whole microtubule system is not understood. Two recent papers use a combination of experimental (imaging) and theoretical (computer simulation) methods to explore the formation of bipolar linear microtubule arrays in fission yeast and the oscillatory movement of the mitotic spindle in the nematode worm. In the simulation approach, the rules for the interactions of the components (microtubules and microtubule-associated proteins) are specified and the evolution of the system is followed, with the aim of identifying the minimal set of components that can mimic the real system. The work on fission yeast concludes that bipolar microtubule structures can arise from self-organization of microtubules through nucleators, bundlers, and sliders, without a requirement for a special microtubule-organizing center. The work on the worm embryo suggests that both the positive feedback that drives oscillations and the centering force that limits their amplitude may arise from microtubule pulling forces. The systems approach exemplified by these papers should stimulate new experiments aimed at discovering the principles of cellular organization.