A Riemannian manifold is called static when it admits a non-trivial solution to a second-order equation that naturally appears both in Geometry (e.g, in the problem of prescribing the scalar curvature) and Physics (e.g., in the study of static black-holes). In this talk we will explain some results towards the classification of static three-manifolds with positive scalar curvature. In these results, we employ minimal surfaces and also explore the correspondence between static three-manifolds manifolds and Einstein four-manifolds (possibly with edge-cone singularities) admitting an isometric circle action of a certain type.