Hydrogen is an attractive automotive fuel because it is carbon-free, abundantly available from water, and has an exceptional mass-energy density. Hydrogen storage has become a trendy topic in recent years with its ability to design low-cost, lightweight materials that can reversibly and rapidly store hydrogen near ambient conditions. Various materials-based systems, such as metal hydrides and metal-organic frameworks (MOFs), have been introduced. This paper discusses and compares each material in terms of hydrogen storage capacity, kinetics, and viability. Different types of metal hydrides, such as magnesium hydrides, complex hydrides, and intermetallic-compounds hydrides, are considered. Furthermore, promising MOFs materials such as zinc- and copper-based MOFs are mentioned. The paper also compares the materials in terms of storage cost, which is rarely discussed in the literature. Results show that metal hydrides require severe pressures and temperatures to achieve optimum storage capacity, which is difficult to obtain and maintain. On the other hand, MOFs have some advantages, such as high surface area, high pore volume, as well as rich open metal sites. However, these properties being offered via MOFs have a limitation of low hydrogen uptake at ambient temperatures for hydrogen storage. This limitation is overcome by designing MOFs with unsaturated open metal sites. Future research is needed to optimize metal hydrides and MOFs to perform better under normal operating conditions to meet the recommendations of the United States Department of Energy.