Hydrogen is widely recognized as a versatile energy carrier with significant potential to support the decarbonization of the power, transport, and industrial sectors. This paper analyzes the integration of hydrogen into power systems and offers an overview of the operation of electrolyzers and fuel cells for readers with limited background in these technologies. Applications of hydrogen beyond the scope of power systems are not considered. Then, this paper explores the mathematical modeling of hydrogen-related technologies, including electrolyzers and fuel cells, to assess their impact on hydrogen production and electricity generation. The paper also reviews recent developments in electricity storage through power-to-gas systems and examines planning models for integrating hydrogen into power systems. Furthermore, the role of hydrogen facilities in power system operations is analyzed in depth. The integration of hydrogen vehicles into power grids is also discussed, emphasizing their diverse applications. Additionally, the paper examines the production of ammonia, which can be used as a fuel for electricity generation. Finally, the most important conclusions of the literature review are summarized, offering an overview of the main findings and identified research gaps.