Bistable Liquid Crystal Displays (LCDs) offer the potential for considerable power savings, compared with conventional (monostable) LCDs. The existence of two (or more) stable field-free states that are optically-distinct means that contrast can be maintained in a display without an externally-applied electric field. An applied field is required only to switch the device from one state to the other, as needed. This dissertation focuses on theoretical models of a possible bistable nematic device, whose operating principle relies on controlling surface anchoring conditions. Switching between the two stable steady states is achieved by application of a transient electric field. A 1D model is considered first, and means are explored, by which the design may be optimized, in terms of optical contrast, manufacturing considerations, switching field strength and switching times. The compromises inherent in these conflicting design criteria are discussed. Motivated by a desire to improve on the results of this 1D model, and to test its robustness, a two-dimensional geometry is considered next, in which variable surface anchoring conditions are used to control the steady-state solutions and it is explored how different anchoring conditions can influence the number and type of solutions, and whether or not switching is possible between the states. A wide range of possible behaviors are found, including bistability, tristability and tetrastability, and it is investigated how the solution landscape changes as the boundary conditions are tuned. All of these investigations are based (for simplicity) on an assumption of uniform electric field within the nematic liquid crystal. To check the validity of this assumption, the study is concluded by formulating the problem with non-uniform field, and comparing the results to the uniform field case.