Widespread adoption of hydrogen as a vehicular fuel depends critically upon the ability to store hydrogen on-board at high volumetric and gravimetric densities, as well as on the ability to extract/insert it at sufficiently rapid rates. As current storage methods based on physical means—high-pressure gas or (cryogenic) liquefaction—are unlikely to satisfy targets for performance and cost, a global research effort focusing on the development of chemical means for storing hydrogen in condensed phases has recently emerged. At present, no known material exhibits a combination of properties that would enable high-volume automotive applications. Thus new materials with improved performance, or new approaches to the synthesis and/or processing of existing materials, are highly desirable. In this critical review we provide a practical introduction to the field of hydrogen storage materials research, with an emphasis on (i) the properties necessary for a viable storage material, (ii) the computational and experimental techniques commonly employed in determining these attributes, and (iii) the classes of materials being pursued as candidate storage compounds. Starting from the general requirements of a fuel cell vehicle, we summarize how these requirements translate into desired characteristics for the hydrogen storage material. Key amongst these are: (a) high gravimetric and volumetric hydrogen density, (b) thermodynamics that allow for reversible hydrogen uptake/release under near-ambient conditions, and (c) fast reaction kinetics. To further illustrate these attributes, the four major classes of candidate storage materials—conventional metal hydrides, chemical hydrides, complex hydrides, and sorbent systems—are introduced and their respective performance and prospects for improvement in each of these areas is discussed. Finally, we review the most valuable experimental and computational techniques for determining these attributes, highlighting how an approach that couples computational modeling with experiments can significantly accelerate the discovery of novel storage materials (155 references).