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.