Methods for measuring the viscosity coefficients of the best known type of anisotropic fluid, nematic liquid crystals (NLCs), are reviewed. The hydrodynamic Leslie-Ericksen-Parodi theory is described in brief, which predicts five independent viscosity coefficients for a NLC. The feature that distinguishes NLCs from isotropic liquids is the rotational viscosity, due to energy dissipation caused by NLC reorientation. The shear flow method, methods based on ultrasonic wave propagation and absorption in an anisotropic medium, and the rotating magnetic field technique are described in detail, as well as methods that involve analyzing the Freedericksz transition dynamics (LC reorientation in an electric or magnetic field) and those using light scattering from the thermal fluctuations of the NLC director. In each case, the accuracy of the method is evaluated, its complexity assessed, and the amount of material needed for measurement estimated.