Radial glia (RG) are the main progenitor cell type in the developing cortex. These cells are highly polarized, with a long basal process spanning the entire thickness of the cortex and acting as a support for neuronal migration. The RG cell terminates by an endfoot that contacts the pial (basal) surface. A shorter apical process also terminates with an endfoot that faces the ventricle, with a primary cilium protruding in the cerebrospinal fluid. These cell domains have particular subcellular compositions that are critical for the correct functioning of RG. When altered, this can affect proper development of the cortex, ultimately leading to cortical malformations, associated with different pathological outcomes. In this review, we focus on the current knowledge concerning the cell biology of these bipolar stem cells and discuss the role of their polarity in health and disease.