Solid polymer electrolytes (SPEs) have attracted significant attention as promising electrolyte systems for all-solid-state batteries due to their excellent interfacial contact and flexible processability. However, their practical application is still limited by low ionic conductivity and insufficient mechanical stability. To address these limitations, the incorporation of inorganic nanofillers into polymer electrolytes has been widely investigated. Nevertheless, conventional filler materials often require complicated synthesis processes and involve high production costs, limiting their large-scale application. As a sustainable alternative, natural clay minerals have recently emerged as attractive nanofillers for SPEs because of their low cost, eco-friendliness, abundant surface active sites, and diverse structural characteristics. In this review, clay mineral-based nanofillers are systematically classified according to their structural morphology into 1D, 2D, and 3D structures. The effects of each morphology on ionic conductivity, lithium-ion transference number, interfacial resistance, electrochemical stability, and mechanical properties are comprehensively discussed. In addition, this review highlights that electrolyte performance is strongly influenced not only by filler morphology but also by interfacial engineering, including surface modification, filler dispersion, and interactions with polymer matrices. Based on these insights, major challenges and future strategies are discussed, such as hybrid structural design, interface control, and filler content optimization to overcome the limitations of morphology-based approaches. Overall, this review provides deeper insight into the structure–performance relationship of clay mineral-based SPEs and offers practical design guidelines for next-generation all-solid-state battery electrolytes.