Replacing human hand function with prostheses goes far beyond only recreating muscle movement with feedforward motor control. Natural sensory feedback is pivotal for fine dexterous control and finding both engineering and surgical solutions to replace this complex biological function is imperative to achieve prosthetic hand function that matches the human hand. This review outlines the nature of the problems underlying sensory restitution, the engineering methods that attempt to address this deficit and the surgical techniques that have been developed to integrate advanced neural interfaces with biological systems. Currently, there is no single solution to restore sensory feedback. Rather, encouraging animal models and early human studies have demonstrated that some elements of sensation can be restored to improve prosthetic control. However, these techniques are limited to highly specialized institutions and much further work is required to reproduce the results achieved, with the goal of increasing availability of advanced closed loop prostheses that allow sensory feedback to inform more precise feedforward control movements and increase functionality.