Hydrogen carriers are one of the keys to the success of using hydrogen as an energy vector. Indeed, sustainable hydrogen production exploits the excess of renewable energy sources, after which temporary storage is required. The conventional approaches to hydrogen storage and transport are compressed hydrogen (CH2) and liquefied hydrogen (LH2), which require severe operating conditions related to pressure (300–700 bar) and temperature (T < −252 °C), respectively. To overcome these issues, which have hindered market penetration, several alternatives have been proposed in the last few decades. In this review, the most promising hydrogen carriers (ammonia, methanol, liquid organic hydrogen carriers, and metal hydrides) have been considered, and the main stages of their supply chain (production, storage, transportation, H2 release, and their recyclability) have been described and critically analyzed, focusing on the latest results available in the literature, the highlighting of which is our current concern. The last section reviews recent techno-economic analyses to drive the selection of hydrogen carrier systems and the main constraints that must be considered. The analyzed results show how the selection of H2 carriers is a multiparametric function, and it depends on technological factors as well as international policies and regulations.