The asymmetric segregation of cell-fate determinants and the generation of daughter cells of different sizes rely on the correct orientation and position of the mitotic spindle. In the Drosophila embryo, the determinant Prospero is localized basally and is segregated equally to daughters of similar cell size during epidermal cell division. In contrast, during neuroblast division Prospero is segregated asymmetrically to the smaller daughter cell. This simple switch between symmetric and asymmetric segregation is achieved by changing the orientation of cell division: neural cells divide in a plane perpendicular to that of epidermoblast division. Here, by labelling mitotic spindles in living Drosophila embryos, we show that neuroblast spindles are initially formed in the same axis as epidermal cells, but rotate before cell division. We find that daughter cells of different sizes arise because the spindle itself becomes asymmetric at anaphase: apical microtubules elongate, basal microtubules shorten, and the midbody moves basally until it is positioned asymmetrically between the two spindle poles. This observation contradicts the widely held hypothesis that the cleavage furrow is always placed midway between the two centrosomes.