Ever since the identification of 6830 and 7088 features as the Raman scattered O VI 1032, 1038 resonance doublets in symbiotic stars by Schmid (1989), Raman scattering by atomic hydrogen has been a very unique tool to investigate the mass transfer processes in symbiotic stars. Discovery of Raman scattered He II in young planetary nebulae (NGC 7027, NGC 6302, IC 5117) allow one to expect that Raman scattering can be an extremely useful tool to look into the mass loss processes in these objects. Because hydrogen is a single electron atom, their wavefunctions are known in closed form, so that exact calculations of cross sections are feasible. In this paper, I review some basic properties of Raman scattered features and present detailed and explicit matrix elements for computation of the scattering cross section of radiation with atomic hydrogen. Some astrophysical objects for which Raman scattering may be observationally pertinent are briefly mentioned.