Digital twin technology, a cornerstone of Industry 4.0, offers a transformative approach to enhancing the safety and reliability of hydrogen systems. By enabling real-time monitoring, predictive maintenance, and optimized operations through virtual replicas of physical assets, digital twins are poised to revolutionize the hydrogen economy. This review highlights significant findings on the application of digital twins within the hydrogen sector, focusing on mathematical modeling techniques, including differential equations, Kalman filters, optimization algorithms, and machine-learning approaches, to accurately represent the complex dynamics of hydrogen production and storage systems. Key results include insights into the implementation of digital twins for gaseous, liquid, and solid-state hydrogen storage, as well as their integration with alkaline, Proton Exchange Membrane electrolyzers, and solid oxide electrolysis technologies. Notable applications explored include material selection, process optimization, and risk assessment. The potential of emerging technologies such as quantum computing, advanced sensor systems, and artificial intelligence to enhance digital twin capabilities is also discussed. To ensure widespread adoption and interoperability, the importance of standardization efforts and the development of open-source platforms is emphasized. This comprehensive review systematically analyzes the current state of digital twins in the hydrogen economy, offering actionable insights for researchers, industry professionals, and policymakers aiming to leverage this technology for a safer and more reliable hydrogen future.