Nowadays, due to a growing number of tissue injuries, in particular, skin wounds, induction and promotion of tissue healing responses can be considered as a crucial step towards a complete regeneration. Recently, biomaterial design has been oriented towards promoting a powerful, effective, and successful healing. Biomaterials with wound management abilities have been developed for different applications such as providing a native microenvironment and supportive matrices that induce the growth of tissue, creating physical obstacles against microbial contamination, and to be used as delivery systems for therapeutic reagents. Until now, numerous strategies aiming to accelerate the wound healing process have been utilized and studied with their own pros and cons. In this review, tissue remodeling phenomena, wound healing mechanisms, and their related factors will be discussed. In addition, different methods for induction and acceleration of healing via cell therapy, bioactive therapeutic delivery, and/or biomaterial-based approaches will be reviewed.