Smart biomaterials have been rapidly advancing ever since the concept of tissue engineering was proposed. Interacting with human cells, smart biomaterials can play a key role in novel tissue morphogenesis. Various aspects of biomaterials utilized in or being sought for the goal of encouraging bone regeneration, skin graft engineering, and nerve conduits are discussed in this review. Beginning with bone, this study summarizes all the available bioceramics and materials along with their properties used singly or in conjunction with each other to create scaffolds for bone tissue engineering. A quick overview of the skin-based nanocomposite biomaterials possessing antibacterial properties for wound healing is outlined along with skin regeneration therapies using infrared radiation, electrospinning, and piezoelectricity, which aid in wound healing. Furthermore, a brief overview of bioengineered artificial skin grafts made of various natural and synthetic polymers has been presented. Finally, by examining the interactions between natural and synthetic-based biomaterials and the biological environment, their strengths and drawbacks for constructing peripheral nerve conduits are highlighted. The description of the preclinical outcome of nerve regeneration in injury healed with various natural-based conduits receives special attention. The organic and synthetic worlds collide at the interface of nanomaterials and biological systems, producing a new scientific field including nanomaterial design for tissue engineering.