Chronic wounds have been a global health threat over the past few decades, requiring urgent medical and research attention. The factors delaying the wound-healing process include obesity, stress, microbial infection, aging, edema, inadequate nutrition, poor oxygenation, diabetes, and implant complications. Biomaterials are being developed and fabricated to accelerate the healing of chronic wounds, including hydrogels, nanofibrous, composite, foam, spongy, bilayered, and trilayered scaffolds. Some recent advances in biomaterials development for healing both chronic and acute wounds are extensively compiled here. In addition, various properties of biomaterials for wound-healing applications and how they affect their performance are reviewed. Based on the recent literature, trilayered constructs appear to be a convincing candidate for the healing of chronic wounds and complete skin regeneration because they mimic the full thickness of skin: epidermis, dermis, and the hypodermis. This type of scaffold provides a dense superficial layer, a bioactive middle layer, and a porous lower layer to aid the wound-healing process. The hydrophilicity of scaffolds aids cell attachment, cell proliferation, and protein adhesion. Other scaffold characteristics such as porosity, biodegradability, mechanical properties, and gas permeability help with cell accommodation, proliferation, migration, differentiation, and the release of bioactive factors.