Let G be an algebraic group acting on a finite-type scheme X; a natural question is whether there exists a categorical quotient $X // G$ of this action as a finite-type scheme. When G is reductive, this is answered by D. Mumford’s Geometric Invariant Theory (GIT), a keystone of contemporary algebraic geometry. In the case where G is no-longer reductive, the problem is more subtle; if the unipotent radical of G admits an internal grading, one may instead invoke results from Non-Reductive GIT, as initially developed by F. Kirwan et. al. In this talk, we will explain how the existence of quotients by internally-graded groups in non-reductive GIT follows from more general existence results for moduli spaces of algebraic stacks of filtered objects, in the sense of D. Halpern-Leistner. Time permitting, we will also indicate how this more general perspective can be used to construct quasi-projective moduli spaces of unstable principal bundles with reductive structure group G, which (when G = GL(n)) simplifies the non-reductive GIT constructions of moduli spaces of unstable vector bundles of J. Jackson, Y. Qiao and V. Hoskins–J. Jackson. This talk is based on joint ongoing work with Ludvig Modin (Hannover)