The field of biomaterials has recently emerged to augment or replace lost or damaged tissues and organs due to the human body’s limited ability to self-heal large defects. Historically, metallic components, polymers, ceramics, and composite materials were utilized as synthetic materials along with natural materials to assist in therapy. Various novel biomaterials were developed to respond to a significant amount of new medical challenges in the past decade. Therefore, there is a need to review these newly developed biomaterials and their potential to improve tissue repair and regeneration in a variety of applications. Here, we briefly review the different strategies and attempts to use novel biomaterials, including self-assembled and macromolecular biomaterials, hydrogels, metamaterials, decellularized tissues, and biomaterials obtained via synthetic biology, used either for tissue repair and regeneration or for therapeutic use by exploiting other mechanisms of healing. All these methods aim to create functional materials, devices, systems, and/or organisms with novel and useful functions on the basis of catalogued and standardized biological building blocks. This review details the various methods and introduces the applications of these biomaterials in tissue repair and regeneration, especially for bone, nerve, and skin applications.