In recent decades, new and improved materials have been developed with a significant interest in three-dimensional (3D) scaffolds that can cope with the diverse needs of the expanding biomedical field and promote the required biological response in multiple applications. Due to their biocompatibility, ability to encapsulate and deliver drugs, and capacity to mimic the extracellular matrix (ECM), typical hydrogels have been extensively investigated in the biomedical and biotechnological fields. The major limitations of hydrogels include poor mechanical integrity and limited cell interaction, restricting their broad applicability. To overcome these limitations, an emerging approach, aimed at the generation of hybrid materials with synergistic effects, is focused on incorporating nanoparticles (NPs) within polymeric gels to achieve nanocomposites with tailored functionality and improved properties. This review focuses on the unique contributions of clay nanoparticles, regarding the recent developments of clay-based nanocomposite hydrogels, with an emphasis on biomedical applications.