The global demand for fossil fuels in the transportation sector is increasing rapidly due to the continuous growth of internal combustion engine vehicles. This leads to severe environmental problems, including greenhouse gas emissions and air-quality deterioration. Thus, it is necessary to increase the use of renewable energy sources in the transportation sector as well as other off-grid applications. Battery and fuel cells are promising alternatives owing to high efficiency and low (even zero) local emissions. However, they are limited by either the low capacity or sluggish dynamic response. These shortcomings can be overcome by the hybridization of battery and fuel cells, which have been the focus of leading international automotive and shipbuilding companies. This paper presents a comprehensive evaluation and comparison of different hybrid systems of Proton Exchange Membrane Fuel Cell with battery and Solid Oxide Fuel Cell with battery for mobility and other off-grid applications from perspectives of system configurations, technical specifications, energy management strategies, and experimental validation. With the existing issues and corresponding solving strategies highlighted, the suggestions for designing high-performance fuel cell hybrid power systems are concluded accordingly. This review can serve as a reference and guide to advance the development of the fuel cell and battery hybrid power systems for mobility and off-grid applications.