Recently there has been an advance in understanding the relationship between the derived categories of the stack quotient of a variety X by a group G and its GIT quotients. I will explain the connection. Then I will present joint work with Dan Halpern-Leistner on how a variation of GIT can be used to produce autoequivalences, which turn out to be special. Along the way, we will see a tight connection between spherical functors and mutations of semiorthogonal decompositions. If time and courage permit, I will remark on how our results confirm a prediction from mirror symmetry.