Two‐dimensional materials have led to a leap forward in materials science research, especially in the fields of energy conversion and storage. Borophene and its spherical counterpart boron fullerene represent emerging materials that have attracted much attention in the whole area of advanced energy materials and technologies. Owing to their prominent features, such as electronic environment and geometry, borophene and boron fullerene have been used in versatile applications, such as supercapacitors, superconductors, anode materials for photochemical water splitting, and biosensors. Herein, one of the most promising applications/areas of hydrogen storage is discussed. Boron fullerenes have been considered and discussed for hydrogen‐storage applications, and recently borophene was also included in the list of materials with promising hydrogen‐storage properties. Studies focus mainly on doped borophene systems over pristine borophene due to enhanced features available upon decoration with metal atoms. This Review introduces very recent progress and novel paradigms with respect to both borophene derivatives and boron fullerene based systems reported for hydrogen storage, with a focus on the synthesis, physiochemical properties, hydrogen‐storage mechanism, and practical applications.