By a spectral mulitplier theorem for a self-adjoint operator L, we mean that the functional calculus F(L) is bounded on L^p for all p (or for some p in an interval arround 2) for functions having minimal regularity. We have in mind Hörmander's condition when L is the Laplace operator on Euclidean space. Several recents works were concerned  by  extensions to non-Euclidean settings or dealing with other operators.  We review some recent results in this direction.