Geometric Invariant Theory (GIT) is the theory of defining quotients in Algebraic Geometry. In his paper https://arxiv.org/abs/1203.0276 (The Derived Category of a GIT quotient) Halpern-Leistner sets up a way of thinking about the derived category of a GIT quotient and in particular gives a semiorthogonal decomposition of the derived category of \$[X/G]\$ where one of the components is the derived category of \$[X^{ss}/G]\$ where \$G\$ is a reductive group, \$X\$ is a variety and \$X^{ss}\$ is the GIT semistable locus. In this talk I will start with a short introduction to GIT and try to give a roadmap to how we get such a semiorthogonal decomposition. It will involve the idea of what are called "window categories" which are extremely important tools being used in this area recently.