In this work a review of the development of compton suppression is presented. It was shown that the application of Compton-suppression counting in instrumental NAA reduces the detection limits and improves the accuracy for a list of elements by substantial reduction of the background of the -spectroscopy. Results for certified reference materials obtained through the use of Compton suppression are normally more accurate and in agreement with the published values. Compton suppression is particularly helpful for low level concentrations in environmental samples to those elements which exhibit severe special interferences in the normal NAA counting. A list of the elements with isotopes having single or close to single -ray decay schemes and which could benefit from Compton-suppression counting is presented. Also, evaluation is made regarding the reliability of Compton suppression with increase in the overall dead-time of the counting. It was concluded that this method does not provide accurate quantification of the isotopes when the overall dead-time exceeds the 10% range. Investigation of the natural background was performed with Compton suppression for the purpose of neutron activation analysis application. The method presented proves to broaden the application of NAA and helps in its competition for simplicity, accuracy and reliability with the modern methods of elemental analysis. Future application of coincidence spectrometry in activation analysis should include better enclosing of the primary detector, utiliza5tion of x-ray and well type detectors, -, -, and -- coincidence techniques.