I will recall a unifying paradigm which incorporates representation theory of semisimple Lie algebras, Weyl algebras, D-modules, Cherednik algebras, and many more. In the case of semisimple Lie algebras, one considers the geometry of the cone of ad-nilpotent elements and its quantization (noncommutative deformation). I will explain how one can study these by a basic algebraic invariant, Poisson homology, and deduce powerful statements such as bounds on the number of finite-dimensional irreducible representations. I will end with some open problems and conjectures, such as on symplectic resolutions.