Clay minerals have attracted increasing attention as low-cost, abundant, and structurally tunable catalyst supports for hydrogen generation reactions. In particular, sodium borohydride (NaBH₄)- based hydrogen generation provides an important platform for evaluating how mineral-derived supports influence catalytic activity, stability, metal dispersion, and interfacial reaction behavior. Among various hydrogen production routes, NaBH₄ hydrolysis and related catalytic hydrogen release processes have gained attention within the broader framework of green hydrogen technologies. In this system, catalyst support design plays a critical role in determining surface accessibility, active-site distribution, charge-transfer behavior, and long-term catalytic performance. This review examines the structural, morphological, physicochemical, and electrochemical roles of clay minerals in clay-supported catalytic systems for hydrogen generation, with particular emphasis on NaBH₄-based systems. The structural classification of phyllosilicates including 1:1 vs. 2:1-layer types, is discussed in relation to their corresponding morphologies, such as plate-like kaolinite, tubular halloysite, and swelling montmorillonite. Particular attention is given to morphology- and surface-chemistry-dependent catalytic mechanisms in NaBH₄ hydrolysis, where surface accessibility, interlayer characteristics, cation exchange capacity, metal-support interactions, and interfacial charge-transfer processes influence hydrogen generation performance. A comparative analysis of reported clay-supported systems published between 2020 and 2025 reveals that while tubular and high-cation-exchange-capacity structures may enhance metal dispersion, reactant diffusion, and catalytic stability. However, catalytic performance is not governed by morphology alone. Instead, metal distribution, thermal treatment effects, surface activation, support conductivity, and structural evolution during catalyst preparation frequently dominate the observed activity trends. By integrating mineralogical structure with catalytic and electrochemical function, this work provides a mechanistic framework for evaluating clay-based systems and discusses their future potential in photocatalytic, UV-responsive, and electrochemically hydrogen generation platforms. The findings highlight that rational catalyst design should consider both intrinsic clay architecture and processing-induced transformations to advance sustainable, mineral-derived catalytic materials for next-generation green hydrogen technologies.