Shark skin surfaces of fast-swimming sharks are characterized as non-smooth because of the presence of dermal denticles or riblet structures and exhibit an excellent drag-reduction effect. A review of the surface morphology, structure and mechanical behaviors of shark skin is given. Investigations into the microstructures of a single denticle and the mechanical behaviors of complete fresh shark skin containing both epidermal and dermal layers were reported. The results show that some nanostructured protuberances exist on the concave groove surface of a denticle. In particular, the complete fresh shark skin exhibits an excellent elasticity, and its stress-strain curve is different from that of the corresponding epidermal layer. Furthermore, the mechanisms of drag reduction by riblets and complaint wall were introduced, various methods of fabricating biomimetic riblet-structured surfaces were classified and summarized, and studies on the drag-reduction effects and applications of biomimetic riblet-structured surfaces were also reviewed. Based on these analyses and on the understanding of the drag-reduction mechanisms, the concept of a synergistic drag-reduction effect that is attributed to a non-smooth surface and an elastic matrix was proposed for the first time.