Despite being the lightest element in the periodic table, hydrogen poses many risks regarding its production, storage, and transport, but it is also the one element promising pollution-free energy for the planet, energy reliability, and sustainability. Development of such novel materials conveying a hydrogen source face stringent scrutiny from both a scientific and a safety point of view: they are required to have a high hydrogen wt.% storage capacity, must store hydrogen in a safe manner (i.e., by chemically binding it), and should exhibit controlled, and preferably rapid, absorption–desorption kinetics. Even the most advanced composites today face the difficult task of overcoming the harsh re-hydrogenation conditions (elevated temperature, high hydrogen pressure). Traditionally, the most utilized materials have been RMH (reactive metal hydrides) and complex metal borohydrides M(BH4)x (M: main group or transition metal; x: valence of M), often along with metal amides or various additives serving as catalysts (Pd2+, Ti4+ etc.). Through destabilization (kinetic or thermodynamic), M(BH4)x can effectively lower their dehydrogenation enthalpy, providing for a faster reaction occurring at a lower temperature onset. The present review summarizes the recent scientific results on various metal borohydrides, aiming to present the current state-of-the-art on such hydrogen storage materials, while trying to analyze the pros and cons of each material regarding its thermodynamic and kinetic behavior in hydrogenation studies.