The Kramer's-Heisenberg approach is well developed for the theory of one phonon resonant Raman scattering (OPRRS) based on both intermediate states of free electrons and correlated electron-hole pairs in 3, 2 and 0-dimensional (D) systems. But to our knowledge, a theory of OPRRS incorporating excitonic effects has not yet been developed for quantum confined 1D system. In this talk we present a generic expression for the resonant Raman scattering cross section from a 1D system explicitly accounting for excitonic effects. We show how the theory is useful for analyzing the Raman resonance excitation profile lineshapes for of a variety of 1D systems. We apply this formalism to simple model systems to the similarities and differences between the free electron and correlated electron-hole 1D theory and also compare with the 3D excitonic theory.