The main aspects of cerebral blood flow regulation are analyzed in the present work. Particular emphasis is given to the biophysical aspects of the cerebral circulation and to problems related with mathematical modeling. Throughout the present work a systemic approach is used, i.e., the intracranial circulation is regarded as a complex system, the behavior of which derives from the interaction and superimposition of several concomitant effects. A brief historical review of the major experimental results on cerebrovascular regulation is presented. Subsequently, the functional structure of the cerebrovascular bed is analyzed in detail and the major feedback regulatory mechanisms, which are now assumed to work on the cerebral circulation (that is, the chemical, the myogenic and the neurogenic ones) are separately examined, according to recently published literature. Mathematical models able to describe all these phenomena are presented and their advantages, limitations, and possible role in physiological investigation discussed. Finally, attention is focused on the major problems which still deserve further studies and on possible lines for future investigations.