Liquid crystals (LCs) have been one of the hot topics in physics, chemistry and material science for decades. Nematic liquid crystals (NLCs) are composed of molecules tending to align in a preferred direction and thus have orientational order. Hence, NLCs possess electromagnetic and optical properties similar to crystals, and play an important role in applications ranging from display to light field regulation, etc. LCs usually contain defects and therein exhibit special optical textures. In order to study these defects, a prevailing method is to build proper theoretical models for the LCs. In this review article, several static models of LCs and their applicable conditions are reviewed. The variation of free energy caused by anchoring energy under the interface effect is also analyzed in detail. Moreover, this article introduces the recent advances of the most widely used Landau-de Gennes Q-tensor model in case of elastic constant L→0 and low temperature limit. Finally, the progress of these theoretical models in practical applications is also discussed.