Moduli problems parameterizing objects with infinite automorphisms (eg. semi-stable vector bundles) often do not admit coarse moduli schemes but may admit moduli schemes identifying certain non-isomorphic objects. I will introduce techniques to study such moduli stacks and address the question of how such moduli schemes can be intrinsically constructed. The crucial ingredient is the notion of a good moduli space for an Artin stack, which generalizes Mumford's geometric invariant theory and characterizes the desired geometric properties of a moduli scheme parameterizing objects with infinite automorphisms.