Compounds containing B─H, C─H, N─H, or O─H bonds with high hydrogen content have been extensively studied as potential hydrogen carriers. Their hydrogen storage performance is largely determined by the nature of these bonds, decomposition pathways, and the properties of the dehydrogenation products. Among these compounds, methanol, cyclohexane, and ammonia stand out due to their low costs and established infrastructure, making them promising hydrogen carriers for large-scale storage and transport. They offer viable pathways for decarbonizing society by enabling hydrogen to serve as a clean energy source. However, several challenges persist, including the high temperatures required for (de)hydrogenation, slow kinetics, and the reliance on costly catalysts. To address these issues, strategies such as chemical modification and catalyst development are being pursued to improve hydrogen cycling performance. This review highlights recent progress in hydrogen carriers with B─H, C─H, N─H, or O─H bonds. It examines the fundamental characteristics of these bonds and carriers, as well as advances in catalyst development. Our objective is to offer a comprehensive understanding of current state of hydrogen carriers and identify future research directions, such as molecular modification and system optimization. Innovations in these areas are crucial to advance hydrogen storage technologies for a large-scale hydrogen deployment.