Nanoclays are layered aluminosilicate nanostructures. Depending upon the chemical composition and microscopic structure, various nanoclay types have been discovered such as montmorillonite, bentonite, kaolinite, halloysite nanoclay, etc. Nanoclays have been organically modified to develop compatibility with polymers. Polymer/nanoclay nanocomposites have prompted significant breakthroughs in the field of nanocomposite technology. Green nanocomposites form an important class of nanomaterials using naturally derived degradable materials as matrix/nanofiller. This review essentially deliberates the fundamentals and effect of nanoclay reinforcements in the green polymer matrices. Naturally derived polymers such as cellulose, starch, natural rubber, poly(lactic acid), etc. have been employed in these nanocomposites. Green polymer/nanoclay nanocomposites have been fabricated using various feasible fabrication approaches such as the solution route, melt processing, in situ polymerization, and others. The significance of the structure-property relationships in these nanomaterials, essential to attain the desired features, has been presented. Green polymer/nanoclay nanocomposites are light weight, inexpensiveness, ecofriendly, have a low cost, and enhanced indispensable physical properties. Consequently, the green polymer/nanoclay nanocomposites have found applications towards sustainability uses, packaging, membranes, and biomedical (tissue engineering, drug delivery, wound healing) sectors. However, thorough research efforts are desirable to extend the utility of the green polymer/nanoclay nanocomposites in future technological sectors.