Nanoclays, 2D layered mineral silicates, have been used for centuries and have retained a prominent role in advancing materials science and technology. This class of materials has gained importance over other layered nanomaterials, owing to their abundance, low cost, diverse morphologies, and multiple chemical compositions, imparting them with exceptional physical and chemical properties. Polymer–clay nanocomposites possess exceptional attributes relative to neat polymers or their composite forms. Incorporating an adequate amount of clay content enhances crucial properties, such as tensile strength, modulus, thermal stability, elasticity, and heat deflection temperature, thereby extending their varied appliances. This review outlines the recent advancements in the performance of polymer-reinforced nanoclay composites, including their structures, chemical compositions, and emergent roles in various fields. The deployment and application of nanoclays in food packaging, water treatment, biomedical applications (tissue engineering, regenerative medicines, and therapeutic antibodies), catalysis, energy storage and conversions, and environmental remediation, among others, are critically appraised, including the emerging and latest applications of nanoclays in 3D printing. Finally, the latest advancements of nanoclay composites in terms of the present challenges and future possibilities for innovative applications are outlined.