Shark skin is composed of denticles, or complex scale-like features, which have been shown to reduce drag in turbulent and laminar flow. The denticle crown features undulating structures called riblets that interact with the turbulent boundary layer to reduce drag. Two mechanisms thought to contribute to the drag-reducing properties of riblets include the lifting of streamwise vortices and the hampering of spanwise vortex interactions to reduce crossflow, which could translate to similar flow mechanisms for denticles. Because of the varied morphologies of dermal denticles on different shark species, which also depend on body location, the impact of these denticle geometries on flow is of interest to the biology community, including related fields such as fluid mechanics and oceanography. This review highlights the past 15 years of manufacturing techniques and experimental measurements of drag over denticle-inspired surface structures, including real shark skin samples and engineered denticles and riblets. State-of-the-art additive manufacturing and other techniques are primarily limited to mm-length denticle scales, which have demonstrated drag reduction in lower flow speeds, under 1 m s-1. New manufacturing approaches can create sub-mm length denticles and nanotextured surface structures, which have achieved reported drag reductions of up to 31%. We synthesize results from the literature to illustrate the drag reduction properties of bioinspired denticles and riblets according to their geometry and flow conditions. Using these trends, we suggest design features and focus areas for future research, such as increasing studies of different denticle morphologies, hydrophobicity, antifouling properties, and acoustic noise reduction. Continued work on bioinspired denticles for drag reduction has wider implications in comparative biology and applications to design more energy-efficient, persistent vehicles for environmental monitoring.