This study aims at investigating three-dimensional subject-specific cerebrospinal fluid (CSF) dynamics in the inferior cranial space, the superior spinal subarachnoid space (SAS), and the fourth cerebral ventricle using a combination of a finite-volume computational fluid dynamics (CFD) approach and magnetic resonance imaging (MRI) experiments. An anatomically accurate 3D model of the entire SAS of a healthy volunteer was reconstructed from high resolution T2 weighted MRI data. Subject-specific pulsatile velocity boundary conditions were imposed at planes in the pontine cistern, cerebellomedullary cistern, and in the spinal subarachnoid space. Velocimetric MRI was used to measure the velocity field at these boundaries. A constant pressure boundary condition was imposed at the interface between the aqueduct of Sylvius and the fourth ventricle. The morphology of the SAS with its complex trabecula structures was taken into account through a novel porous media model with anisotropic permeability. The governing equations were solved using finite-volume CFD. We observed a total pressure variation from -42 Pa to 40 Pa within one cardiac cycle in the investigated domain. Maximum CSF velocities of about 15 cms occurred in the inferior section of the aqueduct, 14 cms in the left foramen of Luschka, and 9 cms in the foramen of Magendie. Flow velocities in the right foramen of Luschka were found to be significantly lower than in the left, indicating three-dimensional brain asymmetries. The flow in the cerebellomedullary cistern was found to be relatively diffusive with a peak Reynolds number (Re)=72, while the flow in the pontine cistern was primarily convective with a peak Re=386. The net volumetric flow rate in the spinal canal was found to be negligible despite CSF oscillation with substantial amplitude with a maximum volumetric flow rate of 109 mlmin. The observed transient flow patterns indicate a compliant behavior of the cranial subarachnoid space. Still, the estimated deformations were small owing to the large parenchymal surface. We have integrated anatomic and velocimetric MRI data with computational fluid dynamics incorporating the porous SAS morphology for the subject-specific reconstruction of cerebrospinal fluid flow in the subarachnoid space. This model can be used as a basis for the development of computational tools, e.g., for the optimization of intrathecal drug delivery and computer-aided evaluation of cerebral pathologies such as syrinx development in syringomelia.