The modeling of fluid flow and transport in biological tissues and networks is characterized by complex geometries, strong multiphysics coupling, and parameter regimes spanning different characteristic time and length scales. In this talk, we discuss such problems in the context of brain fluid dynamics and waste clearance, encompassing hemodynamics in the major arteries, perfusion of the cerebral tissue, and flow of cerebrospinal fluid (CSF) in the ventricular system. For tissue perfusion and CSF flow, we consider a coupled system involving unsteady Stokes equations in fluid-filled cavities and a multi-network poroelastic model in the surrounding tissue, accounting for mass exchange and mechanical interaction among compartments. The spatial discretization is based on a polytopal Discontinuous Galerkin method, which naturally handles arbitrary polyhedral elements to allow an efficient compromise between geometrical accuracy and computational effort, particularly relevant in dealing with patient-specific geometries. We discuss numerical properties of the proposed method, including stability and optimal convergence, as well as robustness with respect to heterogeneous physical parameters. For blood flow in major cerebral arteries, we adopt 1D fluid-structure interaction equations in a network modeling the circle of Willis. A comparison between a conforming numerical method and a discontinuous Galerkin method with different numerical fluxes is presented, showing the stability and conservation properties of the different schemes and highlighting their suitability for coupling this model with the 3D tissue perfusion model, with a strategy inherited from cardiovascular applications.