This paper provides a detailed review of renewably driven hydrogen systems and modeling approaches applicable to these systems that have been reported over the last two decades. Several renewable energy technologies, including solar photovoltaic, wind, and hydro, have been considered as the power source in these reports. Storage is an important aspect of hydrogen systems, and options for this are summarized here. Utilization systems include fuel cells as well as a variety of thermal uses. Some of the reported studies have addressed residential applications whereas others were related to commercial scale systems. This paper particularly emphasizes aspects of modeling of the various components for the renewable hydrogen system. Based on the literature on this area, conclusions are provided on the current understanding as well as future work related to this topic.