Computer simulation of the cerebral circulation has been carried out for three decades. We review the developments of cerebral circulation computer models of the last 30 years. Existing models are discussed in terms of fluid dynamics and possible clinical usage. Also the status and new achievements in some related research areas are summarized. Any new achievements in such areas would contribute to the progress of building a better model. A patient specific, highly predictive and reflective model could be a powerful clinical tool which would greatly benefit neurosurgeons and patients.