Semi-orthogonal decompositions of derived categories of coherent sheaves on varieties provide an efficient and flexible means of capturing deep geometric ties to between varieties. I will describe semi-orthogonal decompositions relating the derived categories of GIT quotients obtained via different linearizations of the action. As an application, I will show how to construct full exceptional collections on some moduli spaces of pointed rational curves. This is joint work with D. Favero (Wien) and L. Katzarkov (Miami/Wien).