The intricate process of wound healing involves activation of biological pathways that work in concert to regenerate a tissue microenvironment consisting of cells and external cellular matrix (ECM) with enzymes, cytokines, and growth factors. Distinct stages characterize the mammalian response to tissue injury: hemostasis, inflammation, new tissue formation, and tissue remodeling. Hemostasis and inflammation start right after the injury, while the formation of new tissue, along with migration and proliferation of cells within the wound site, occurs during the first week to ten days after the injury. In this review paper, we discuss approaches in tissue engineering and regenerative medicine to address each of these processes through the application of biomaterials, either as support to the native microenvironment or as delivery vehicles for functional hemostatic, antibacterial, or anti-inflammatory agents. Molecular therapies are also discussed with particular attention to drug delivery methods and gene therapies. Finally, cellular treatments are reviewed, and an outlook on the future of drug delivery and wound care biomaterials is provided.