-Better understanding of the determinants of cerebral blood flow (CBF) and the interpretation of clinical measurements can benefit from quantitative modelling of CBF regulatory mechanisms and their interaction with other haemodynamic variables such as intracranial pressure and blood gases. Mathematical models have been able to reproduce many known phenomena and to extract relevant parameters for patient management. "Black-box" models, chiefly transfer function analysis, are easier to apply in a clinical setting, but cannot separate the contributions of the myogenic, metabolic, or neurogenic regulatory mechanisms from that of the vascular bed and other intracranial elements. Future work should emphasize i) multivariate system identification approaches and, ii) closer collaboration between the mathematical and "black-box" schools of modelling to enhance the benefits of these distinct approaches.