We will study the behaviour of lower scalar curvature bounds under local deformations of the underlying Riemannian metrics. A major application is the preservation of positive scalar curvature metrics under surgeries of codimension at least three, a famous result due to Gromov-Lawson and Schoen-Yau. Combined with bordism theoretic computations, this leads to a powerful construction machine for positive scalar curvature metrics and very general existence results.