In vertebrate somatic cells the centrosome functions as the major microtubule-organizing center (MTOC), which splits and separates to form the poles of the mitotic spindle. However, the role of the centriole-containing centrosome in the formation of bipolar mitotic spindles continues to be controversial. Cells normally containing centrosomes are still able to build bipolar spindles after their centrioles have been removed or ablated. In naturally occurring cellular systems that lack centrioles - such as plant cells and many oocytes - bipolar spindles form in the complete absence of canonical centrosomes. These observations have led to the notion that centrosomes play no role during mitosis. However, recent work has re-examined spindle assembly in the absence of centrosomes, both in cells that naturally lack them, and those that have had them experimentally removed. The results of these studies suggest that an appreciation of microtubule network organization- both before and after nuclear envelope breakdown (NEB) - is the key to understanding the mechanisms that regulate spindle assembly and the generation of bipolarity.