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The intrinsic resolution or minimum line width attainable in NaI(TI) spectrometers can now be set at 5-6% for 662 KeV gamma-rays from Cs-137. Work leading to this conclusion is reviewed. Pressure effects and directional effects in sodiuam iodide which support the exciton energy transport theory (Seitz model) are reported. Also, decay time., temperature coefficient (-0.12% OC), and non-proportional scintillation response in NaI(TI) are reported. Studies of the CsI(Tl) emission spectra and decay time constants as functions of temperature and dE/dx are reported. Separation of alpha from gamma-ray events by color discrimination as well as by pulse shape discrimination is described. A statistical method of measuring decay time constants over a wide range of intensity during decay is presented in an appendix.