In this talk, I will discuss the basic theory of liquid crystals, the theory of the Q-tensor model for liquid crystal dynamics, and various models of the elastic and thermotropic energy of liquid crystal samples. In particular, I will outline a model presented by Golovaty et al. in a 2020 paper which reduces to the Oseen-Frank director field model in uniaxial states. I will then show an energy stable scheme for the gradient flow of a closely related model, discuss a proof of its convergence via fixed-point iteration, and discuss a proof of the Gamma-convergence of discrete minimizers as the mesh size approaches zero. Finally, I will show the results of numerical experiments which successfully simulate isotropic-to-nematic phase transitions as expected.