Given a smooth projective variety defined over a number field or the
function field of a curve over a finite field/complex numbers, a basic
question is to understand the structure of the set of rational points, e.g.,
if the set is non-empty, and if the variety has enough rational points to
approximate the adelic points, i.e. if the variety satisfies weak
approximation. In this talk I will discuss some recent results about weak
approximation properties of cubic hypersurfaces defined over these fields.