In the framework of the renormalization-group (RG) approach, several critical phenomena can be investigated by studying the RG flow of an effective Landau-Ginzburg-Wilson (LGW) Phi4 theory, having an N-component order parameter as fundamental field, and containing up to 4th-order polynomials of the field. I discuss the general properties of the RG flow in these theories, and present an overview of RG field-theory results for physically interesting LGW Phi4 theories, whose results apply to critical phenomena in liquids, magnets, disordered and/or frustrated spin systems, to the finite-T transition in hadronic matter, etc...