The mitotic spindle uses dynamic microtubules and mitotic motors to generate the pico-Newton scale forces that are needed to drive the mitotic movements that underlie chromosome capture, alignment and segregation. Here, we consider the biophysical and molecular basis of force-generation for chromosome movements in the spindle, and, with reference to the Drosophila embryo mitotic spindle, we briefly discuss how mathematical modeling can complement experimental analysis to illuminate the mechanisms of chromosome-to-pole motility during anaphase A and spindle elongation during anaphase B.