Although granular materials are predominantly plastic, preparation-dependent, anisotropic under shear, and incrementally nonlinear, their static stress distribution is well accounted for, in the whole range up to the point of failure, by an isotropic, nonlinear and carefully tailored elasticity theory termed GE, for "granular elasticity". Its usefulness, limits, and the understanding behind it are reviewed, and some contentious questions (e.g. what is the elastic reference state, how to measure the elastic displacement) discussed.