This talk focuses on the issues that arise when modeling and simulating fluids containing rod--like molecules (nematics). The (average) orientation of these fluids is typically modeled by a unit vector field which complicates both the analysis and numerical solution of these equations. In particular, i) The unit length constraint gives rise to topological singularities. While singularities are observed ubiquitously in liquid crystals, classical models assign infinite elastic energy to these configurations. ii) In a numerical context, imposing the unit length constraint can lead to ``locking''; that is, too few polynomial functions exist which satisfy the constraint. iii) The the unit length constraint is frequently relaxed to accommodate the formation of singularities with finite energy or isotropic regions. However, there is not definitive physical principle to determine the evolution of the phases. iv) The head--to--tail symmetry of the nematic molecules allows them to form non--orientable direction fields and degree half singularities, so director take values in real projective space. v) Currently there is no ``St. Venant'' principle guaranteeing that the flow and director configuration away from a singularity is not sensitive to the fine structure of the core. The development of numerical schemes in this context will be discussed.