Hydrogen is one of the cleanest energies with potential to have zero carbon emission. Hydrogen storage is a challenging phase for the hydrogen energy application. The safety, cost, and transportation of compressed and liquified hydrogen hinder the widespread application of hydrogen energy. Chemical absorption of hydrogen in solid hydrogen storage materials is a promising hydrogen storage method due to its high storage and transportation performance. Hydrogen storage density, dehydrogenation temperature, and dehydrogenation dynamics are the main challenges for the hydrogen storage materials. The ultimate goal of the system gravimetric capacity was set by the Department of Energy to be 6.5 wt % with a working temperature from -40 to 60 degrees C. The theoretical densities of most present hydrogen storage materials are even lower than 6.5 wt %, which make it impossible to reach the system gravimetric capacity goal. Only hydrogen storage materials with high theoretical density (>= 10 wt %) with further modification have the possibility to reach the goal. However, most of the reviews focus on the research progress of general hydrogen storage materials investigated, many of which have low density. Hydrogen storage materials with high theoretical density including metal borohydrides, metal alanates, ammonia borane, metal amides, and amine metal borohydrides have been reviewed in this article. The pyrolysis and hydrogen absorption conditions of the hydrogen storage materials have been summarized, especially the improvements of the hydrogen storage materials. Furthermore, the challenges of the hydrogen storage materials have been pointed out. Potential hydrogen storage materials and possible modification methods have also been presented and discussed.