In this talk, I will talk about my construction of relative moduli spaces of stable sheaves over the stack of quasipolarized surfaces. For this, I first retrace some of the classical results in the theory of moduli spaces of sheaves on surfaces to make them work over the nonample locus. Then I will recall the theory of good moduli spaces, whose study was initiated by Alper and concerns an intrinsic (stacky) reformulation of the notion of good quotients from GIT. Finally, I use a criterion by Alper-Heinloth-Halpern-Leistner to prove existence of the good moduli space. The application of the construction that I have in mind is extending the Strange Duality results to degree two K3 surfaces - this part is still work in progress.