Abstract: In this talk, we explore geometric and analytic aspects of metric spaces that are homeomorphic to smooth manifolds. Such spaces, often called metric manifolds, arise naturally in geometry, geometric group theory, and analysis on metric spaces. We introduce the notion of a metric fundamental class, which provides an analytic representative of the topological fundamental class, and investigate conditions under which it exists. We then discuss some of the motivations behind studying metric fundamental classes and highlight applications to Lipschitz volume rigidity and isoperimetric inequalities.