Abstrakt: Scalar curvature is a very weak and flexible local invariant in Riemannian geometry. So it is surprising that coupling lower scalar curvature bounds with seemingly harmless topological conditions can recover very powerful rigidity statements, such as Llarull?s theorem or the positive mass theorem. In this talk I will begin by introducing some aspects related to the comparison geometry of lower scalar curvature bounds, focussing in particular on Llarull?s theorem. After this I will discuss a recent rigidity theorem in this setting. This is joint work with Thomas Tony.