**Abstract:**
I will review the renormalization of the interaction of non-relativistic bosons with Dirac-delta function centers in two and three dimensions. It will be explained how the renormalization procedure can be generalized to Riemannian manifolds through the use of the heat kernel. Existence of the ground state and the fact that it's energy is bounded from below will be proven. Renormalization group equations will be derived and the beta function will be calculated. In the second part of the talk, I will expound on how the same ideas are applied to the interaction of relativistic bosons with Dirac-delta function centers in two dimensions, in the Hamiltonian picture.