Prosthetic hands, today, have anthropomorphic, multifinger design. A common control method uses pattern recognition of electromyogram signals. However, these prostheses do not capture the human hand's sensory perception, which is critical for prosthesis embodiment and dexterous object manipulation. This problem can be solved by sensorized electronic skin (e-skin) composed of various sensors that transduce sensory percepts such as touch, pressure, temperature, and pain, just as human skin does. This review will present the physiology of the receptors that encode tactile, thermal, nociceptive, and proprioceptive information. The e-skin is designed to mimic these receptors and their responses. We review each sensor subtype, and its design and performance when embedded in the e-skin. Next, we review the spiking response of the receptors, which are then relayed to sensory nerves and encoded by the brain as sensory percepts. The e-skin system is designed to produce neuromorphic or receptorlike spiking activity. Computational models to mimic these sensory nerve signals are presented and then various methods to interface with the nervous system are explored and compared. We conclude the review with the state of the art in e-skin design and deployment in closed-loop applications that demonstrate the benefits of sensory feedback for amputees.