Liquid crystals are a typical type of soft matter that are intermediate between conventional crystalline solids and isotropic fluids. The nematic phase is the simplest liquid crystal phase, and has been studied the most in the mathematical community. There are various continuum models to describe liquid crystals of nematic type, and $Q$-tensor theory is one among them. The aim of this paper is to give a brief review of recent PDE results regarding the $Q$-tensor theory in dynamic configurations.