Inherent challenges regarding the rheological characterization of slurries of elongated particles have necessitated the development of alternatives to standardized rheometers. These methods of measurement, and the associated advances in the quantification of shear and normal stress measurements, are described. Also, recent advances in modeling and predictive capabilities are summarized. During shearing flows, confinement substantially influences the orientation distribution of the particles; this change in the microstructure impacts the rheology, even as the smallest confining dimension exceeds seven particle lengths. The slow development of the orientation distributions renders additional difficulties in evaluating the rheology. Achievements of the measurement methods include a universal shear viscosity as a function of concentration for a wide range of particle lengths to diameters (aspect ratios). The jamming limit (divergence of the viscosity with concentration) of the suspensions has been also shown to scale differently than for spheres. More general dynamics of the suspensions and the additional needs for measurement improvements are discussed.