The one-cell Caenorhabditis elegans embryo divides asymmetrically into a larger and smaller blastomere, each with a different fate. How does such asymmetry arise? The sperm-supplied centrosome establishes an axis of polarity in the embryo that is transduced into the establishment of anterior and posterior cortical domains. These cortical domains define the polarity of the embryo, acting upstream of the PAR proteins. The PAR proteins, in turn, determine the subsequent segregation of fate determinants and the plane of cell division. We address how cortical asymmetry could be established, relying on data from C. elegans and other polarized cells, as well as from applicable models. We discuss how cortical polarity influences spindle position to accomplish an asymmetric division, presenting the current models of spindle orientation and anaphase spindle displacement. We focus on asymmetric cell division as a function of the actin and microtubule cytoskeletons, emphasizing the cell biology of polarity.