The stress-energy tensor is a rank (0, 2) tensor, denoted $T_{ab},$ that contains information about how a field theory transforms under local diffeomorphisms. This post explains the properties of the stress tensor that I think are of most fundamental importance. In section 1, I take up the issue of what it means for a diffeomorphism to act on a field. I discuss push-forwards of tensor fields under diffeomorphisms, and the linear transformations that are sometimes used to supplement push-forwards in theories where doing so gives a symmetry of the Lagrangian. In section 2, I define the stress tensor in classical field theory, and derive the main equation it satisfies: that when all fields in a theory are pushed forward infinitesimally by a local diffeomorphism $\xi^a,$ the change in the action is $$\delta_{\xi} S = \int_{\mathcal{M}} \xi^b \nabla^a T_{ab} \boldsymbol{\epsilon}.$$ In section 3, I discuss the stress tensor in quantum field theory, and how it can differ from its classical