The extraction of useful minerals or geological materials from the Earth’s crust, most typically from various sources, is crucial to a country’s development and progress. Mineral-rich countries use these resources to transform their economies and propel them toward long-term prosperity. There is an urgent need for the world to increase mineral exploration efforts, improve the recycling of important metal-containing resources, and extract them using upgraded hydrometallurgical procedures with high recovery efficiency. This review paper highlights the importance of strategic and critical metals in the economy and the role of nuclear techniques in the analysis, process optimization, and remediation of metals using solvent extraction, adsorption, and chromatographic resins. Radiotracer analysis, X-Ray Fluorescence spectrometry (XRF), Neutron Activation Analysis (NAA), and X-Ray Diffraction (XRD) are appropriate for improving laboratory-based hydrometallurgical processes, with future technical and economic benefits. The development and installation of novel instruments to provide the real-time control of mining and mineral processing plants for improved control have the potential to aid in the recovery of a broad range of metals.