The cerebrovascular system continuously delivers oxygen and energy substrates to the brain, which is one of the organs with the highest basal energy requirement in mammals. Discontinuities in the delivery lead to fatal consequences for the brain tissue. A detailed understanding of the structure of the cerebrovascular system is important for a multitude of (patho-)physiological cerebral processes and many noninvasive functional imaging methods rely on a signal that originates from the vasculature. Furthermore, neurodegenerative diseases often involve the cerebrovascular system and could contribute to neuronal loss. In this review, we focus on the cortical vascular system. In the first part, we present the current knowledge of the vascular anatomy. This is followed by a theory of topology and its application to vascular biology. We then discuss possible interactions between cerebral blood flow and vascular topology, before summarizing the existing body of the literature on quantitative cerebrovascular topology.