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The characteristic shapes of the response functions of a sodium iodide scintillation spectrometer determine the potential of the spectrometer for X or gamma-ray spectroscopy. The present report reviews the evaluation of these functions for monoenergetic X rays and the limitations placed by this evaluation on the quality of the results for various applications. Emphasis is given to theoretical and experimental methods at X-ray energies between 1 and 100 mev. The theoretical methods available up to 4.5 mev are either of the analytical or Monte Carlo types. Above 4.5 mev, no satisfactory theoretical approaches have been developed. Experimental methods using gamma-ray sources, monoenergetic electron data to synthesize X-ray responses, and synchrotron bremsstrahlung are reviewed in detail.