Boron nitride nanostructures (BNNs), including nanotubes, nanosheets, and nanoribbons, are renowned for their exceptional thermal stability, chemical inertness, mechanical strength, and high surface area, making them suitable for advanced material applications. Metal–organic frameworks (MOFs), characterized by their porous crystalline structures, high surface area, and tunable porosity, have emerged as excellent candidates for gas adsorption and storage applications, particularly in the context of hydrogen. This paper explores the synthesis and properties of BNNs and MOFs, alongside the innovative approach of integrating BNNs within MOFs to create composite materials with synergistic properties. The integration of BNNs into MOFs enhances the overall thermal and chemical stability of the composite while improving hydrogen sensing and storage performance. Various synthesis methods for both BNNs and MOFs are discussed, including chemical vapor deposition, solvothermal synthesis, and in situ growth, with a focus on their scalability and reproducibility. Furthermore, the mechanisms underlying hydrogen sensing and storage are examined, including physisorption, chemisorption, charge transfer, and work function modulation. Electrochemical characterization techniques, such as cyclic voltammetry, electrochemical impedance spectroscopy, and galvanostatic charge–discharge, are used to analyze the performance of BNN-MOF systems in hydrogen storage and sensing applications. These methods offer insights into the material’s electrochemical behavior and its potential to store hydrogen efficiently. Potential industrial applications of BNN-MOF composites are highlighted, particularly in fuel cells, hydrogen-powered vehicles, safety monitoring in hydrogen production and distribution networks, and energy storage devices. The integration of these materials can contribute significantly to the development of more efficient hydrogen energy systems. Finally, this study outlines key recommendations for future research, which include optimizing synthesis techniques, improving the hydrogen interaction mechanisms, enhancing the stability and durability of BNN-MOF composites, and performing comprehensive economic and environmental assessments. BNN-MOF composites represent a promising direction in the advancement of hydrogen sensing and storage technologies, offering significant potential to support the transition toward sustainable energy systems and hydrogen-based economies.