Graphene is an ultimate membrane that mixes both flexibility and mechanical strength, together with many other remarkable properties. A good knowledge of the elastic properties of graphene is prerequisite to any practical application of it in nanoscopic devices. Although this two-dimensional material is only one atom thick, continuous-medium elasticity can be applied as long as the deformations vary slowly on the atomic scale and provided suitable parameters are used. The present paper aims to be a critical review on this topic that does not assume a specific pre-knowledge of graphene physics. The basis for the paper is the classical Kirchhoff-Love plate theory. It demands a few parameters that can be addressed from many points of view and fitted to independent experimental data. The parameters can also be estimated by electronic structure calculations. Although coming from diverse backgrounds, most of the available data provide a rather coherent picture that gives a good degree of confidence in the classical description of graphene elasticity. The theory can than be used to estimate, e.g., the buckling limit of graphene bound to a substrate. It can also predict the size above which a scrolled graphene sheet will never spontaneously unroll in free space.