In all eukaryotes, morphogenesis of the microtubule cytoskeleton into a bipolar spindle is required for the faithful transmission of the genome to the two daughter cells during division. This process is facilitated by the intrinsic polarity and dynamic properties of microtubules and involves many proteins that modulate microtubule organization and stability. Recent work has begun to uncover the molecular mechanisms behind these dynamic events. Here we describe current models and discuss some of the complex repertoire of factors required for spindle assembly and chromosome segregation.