Hydrogen as a sustainable solution is emerging as a key low-carbon fuel for gas turbines, supporting the global trends to move toward decarbonized energy systems. Leading energy companies are actively advancing hydrogen-based technologies. This article presents the current state of knowledge related to the use of hydrogen in gas turbines. This review summarizes recent progress in hydrogen combustion and co-combustion with natural gas, focusing on physicochemical properties, combustion mechanisms, operational challenges, and technological solutions. Compared to methane, hydrogen exhibits a high flame speed, wide flammability limits, and low ignition energy, which enhances lean combustion. These advantages have encouraged major manufacturers, such as Siemens Energy with the SGT-400 (2023) and GE Vernova with the LM6000VELOX (2024), to pursue 100% hydrogen combustion. However, these properties also increase the risks of flashback, combustion instability, and NOx formation. In addition, economic considerations and required combustor design modifications due to high-temperature operation make hydrogen–methane co-firing a more practical near-term solution. Co-firing enables gradual integration, where moderate hydrogen fractions require limited modifications, while higher concentrations necessitate significant redesign and raise material concerns such as hydrogen embrittlement. Advances in CFD, LES, and machine learning have improved predictive capabilities, supported by experimental and industrial validation. Overall, hydrogen-fueled gas turbines represent a promising pathway for flexible and sustainable power generation.