Biopolymers are materials obtained from a natural origin, such as plants, animals, microorganisms, or other living beings; they are flexible, elastic, or fibrous materials. Polysaccharides and proteins are some of the natural polymers that are widely used in wound dressing applications. In this review paper, we will provide an overview of biopolymers and synthetic polymer-based nanocomposites, which have promising applications in the biomedical research field, such as wound dressings, wound healing, tissue engineering, drug delivery, and medical implants. Since these polymers have intrinsic biocompatibility, low immunogenicity, non-toxicity, and biodegradable properties, they can be used for various clinical applications. The significant advancements in materials research, drug development, nanotechnology, and biotechnology have laid the foundation for changing the biopolymeric structural and functional properties. The properties of biopolymer and synthetic polymers were modified by blending them with nanoparticles, so that these materials can be used as a wound dressing application. Recent wound care issues, such as tissue repairs, scarless healing, and lost tissue integrity, can be treated with blended polymers. Currently, researchers are focusing on metal/metal oxide nanomaterials such as zinc oxide (ZnO), cerium oxide (CeO₂), silver (Ag), titanium oxide (TiO₂), iron oxide (Fe₂O₃), and other materials (graphene and carbon nanotubes (CNT)). These materials have good antimicrobial properties, as well as action as antibacterial agents. Due to the highly antimicrobial properties of the metal/metal oxide materials, they can be used for wound dressing applications.