What are these Sum Rules Good For?

Dispersive sum rules, of which the Drell-Hearn-Gerasimov sum rule is a special example, are a consequence of rather general principles. On the one hand, they can be used to make tests of these fundamental principles, allowing to probe deep mysteries of nature. On the other hand, they can be used to access experimental observables that are otherwise impossible to measure, and thus providing excellent opportunities to learn about the physics of strongly interacting systems, such as nucleons and nuclei. I will use examples to illustrate these points.