Skein algebras are certain diagrammatically defined algebras spanned by tangles drawn on the cylinder of a surface, with multiplication given by stacking diagrams. Quantum cluster algebras are certain systems of mutually birational quantum tori whose defining relations are encoded in a quiver drawn on the surface. The category of quantum characters heaves is a q-deformation of the category of a d-equivariant D-modules on the group G, expressed through an algebra D q (G) of “q-difference” operators on G. In this I talk I will explain that these are in fact three sides of the same coin–namely they each arise as different flavors of factorization homology, and hence fit in the framework of four-dimensional topological field theory.