The mitotic spindle is a fascinating protein machine that uses bipolar arrays of dynamic microtubules and many mitotic motors to coordinate the accurate segregation of sister chromatids. Here we discuss recent mathematical models and computer simulations that, in concert with experimental studies, help explain the molecular mechanisms by which the spindle machinery performs its crucial functions. We review current models of spindle assembly, positioning, maintenance and elongation; of chromosome capture and congression; and of the spindle assembly checkpoint. We discuss some limitations of the application of modeling to other aspects of mitosis and the feasibility of building more comprehensive system-level models.