Neutron detection is increasingly vital in various fields such as homeland security, medical sciences, and high-energy physics. However, interference from accompanying gamma rays poses a critical challenge in discrimination. Neutron-gamma discrimination in a mixed radiation field is the major challenge with neutron detectors, especially with organic scintillators. In this context, various approaches, both classical and advanced, have been suggested to address this challenge. The purpose of this paper is to provide readers from various backgrounds with a structured view of these approaches for neutron-gamma discrimination, using different types of organic scintillators. Selected reference works are reviewed in this prospect. Then, a comparison study of these methods according to accuracy and type of detector is conducted. Finally, an analysis of the latest advanced methods is provided. Potential recommendations to the research community are outlined.