Abstract
In this chapter we explain the rationale behind the theoretical modeling of liquid crystals and explain the important steps to construct a realistic and accurate model for a particular physical system. We then summarize two commonly used theories of nematics: one based on using the director as a dependent variable and one based on using the tensor order parameter. Using an example problem, the pi-cell, we show the advantages and disadvantages of these two theoretical approaches, demonstrating the importance of carefully considering the choice of model before embarking on simulations.