State-of-the-art prosthetic hands nearly match the dexterity of the human hand, and sophisticated approaches have been developed to control them intuitively. However, grasping and dexterously manipulating objects relies heavily on the sense of touch, without which we would struggle to perform even the most basic activities of daily living. Despite the importance of touch, not only in motor control but also in affective communication and embodiment, the restoration of touch through bionic hands is still in its infancy, a shortcoming that severely limits their effectiveness. Here, we focus on approaches to restore the sense of touch through an electrical interface with the peripheral nerve. First, we describe devices that can be chronically implanted in the nerve to electrically activate nerve fibers. Second, we discuss how these interfaces have been used to convey basic somatosensory feedback. Third, we review what is known about how the somatosensory nerve encodes information about grasped objects in intact limbs and discuss how these natural neural codes can be exploited to convey artificial tactile feedback. Finally, we offer a blueprint for how these codes could be implemented in a neuroprosthetic device to deliver rich, natural, and versatile tactile sensations.