Prompt gamma-ray neutron activation analysis (PGNAA) is a powerful, non-destructive technique widely used for multi-elemental analysis, valued for its rapid, on-site measurement capability and high sensitivity across diverse elements. Based on neutron capture reactions, PGNAA enables precise identification and quantification of elements by detecting characteristic prompt gamma emissions from neutron-captured nuclei. Recent advances in computational modeling, including Monte Carlo simulations, have revolutionized PGNAA setup design, allowing optimized configurations that enhance measurement accuracy and significantly reduce background noise. PGNAA's versatility has led to its adoption in critical applications, including food and agriculture, environmental monitoring, industrial process control, and security screening. This review covers PGNAA's setup, covering essential components such as neutron sources, moderators, collimators, and gamma detection, and highlights modern optimization techniques like machine learning and genetic algorithms. These transformative methods have boosted PGNAA's signal-to-noise ratio and enabled precise, efficient system designs. Additionally, parametric and sensitivity analyses, including the Morris method, are critical in refining system robustness under diverse operational conditions. Advanced data processing approaches, such as noise-mitigation preprocessing and post-processing, further improve the reliability of the information extracted. Despite its many strengths, PGNAA faces challenges, such as reducing background noise interference preserving high sensitivity and specificity, ensuring compact and deployable system designs, and meeting safety and regulatory standards are all crucial to the success of PGNAA detection systems. This review provides a comprehensive overview of PGNAA, addressing these practical criteria and identifying future directions to broaden its application potential in advanced analytical fields.