General potential theories concern the study of functions which are subharmonic with respect to a suitable constraint set in the space of 2-jets. While interesting in their own right, general potential theories are being widely used to study fully nonlinear PDEs determined by degenerate elliptic operators acting on the space of 2-jets. We will discuss a powerful tool, the Correspondence Principle, which establishes the equivalence between subharmonics/superharmonics u and admissible subsolutions/supersolutions u (in the viscosity sense) of the PDE determined by every operator which is compatible with the constraint set. The crucial degenerate ellipticity often requires the operator to be restricted to a suitable constraint set, which determines the admissibility. Applications to comparison principles by way of the duality-monotonicity-fiberegularity method will also be discussed. The results to be presented have been obtained in collaboration with Marco Cirant, Reese Harvey, Blaine Lawson and Davide Redaelli.