  The notion of Nonlocal Mean Curvature (NMC) appears recently in the
mathematics literature. It is an extrinsic geometric quantity that is invariant
under global reparameterization of a surface and provide a natural extension of
the classical mean curvature. We describe some properties of the NMC and the
quasilinear differential operators that are involved when it acts on graphs. We
also survey recent results on surfaces having constant NMC and describe their
intimate link with some problems arising in the study of overdetermined
boundary value problems.
