Many vital processes taking place in electrolytes, such as nanoparticle self-assembly, water purification, and the operation of aqueous supercapacitors, rely on the precise many-body interactions between surfaces and ions in water. Here we study the interaction between a hydrated ion and a charge-neutral graphene layer using atomistic molecular dynamics simulations. For small separations, the ion–graphene repulsion is of nonelectrostatic nature, and for intermediate separations, van der Waals attraction becomes important. Contrary to prevailing theory, we show that nonlinear and tensorial dielectric effects become non-negligible close to surfaces, even for monovalent ions. This breakdown of standard isotropic linear dielectric theory has important consequences for the understanding and modeling of charged objects at surfaces.