Monotonicity formulas in potential theory with applications

We present an overview of some new monotonicity formulas, holding in the realm of linear and nonlinear potential theory, together with their main applications to several domains of investigation. These are ranging from the theory of overdetermined boundary value problems in the classical Euclidean setting, to the classification of static black holes in general relativity and to the geometry of manifolds with nonnegative Ricci curvature. (Joint works with V. Agostiniani, M. Fogagnolo and A. Pinamonti).