I will first review results established by Aizenman, Fröhlich and Duminil-Copin on the triviality of one (- or two) component scalar field theory  in d>=4 dimensions. Then I will present a new approach introduced by Kopper using the flow equations of the renormalization group . We study a real scalar field with varphi^4 self-interaction of N vector components in 4 dimensions in the mean field approximation. For the massive theory we prove triviality for any value of the bare couplings and of N. We also elucidate the relation between triviality and (nontrivial) renormalized perturbation theory.