The feeling of embodiment, i.e., experiencing the body as belonging to oneself and being able to integrate objects into one's bodily self-representation, is a key aspect of human self-consciousness and has been shown to importantly shape human cognition. An extension of such feelings toward robots has been argued as being crucial for assistive technologies aiming at restoring, extending, or simulating sensorimotor functions. Empirical and theoretical work illustrates the importance of sensory feedback for the feeling of embodiment and also immersion; we focus on the the perceptual level of touch and the role of tactile feedback in various assistive robotic devices. We critically review how different facets of tactile perception in humans, i.e., affective, social, and self-touch, might influence embodiment. This is particularly important as current assistive robotic devices - such as prostheses, orthoses, exoskeletons, and devices for teleoperation-often limit touch low-density and spatially constrained haptic feedback, i.e., the mere touch sensation linked to an action. Here, we analyze, discuss, and propose how and to what degree tactile feedback might increase the embodiment of certain robotic devices, e.g., prostheses, and the feeling of immersion in human-robot interaction, e.g., in teleoperation. Based on recent findings from cognitive psychology on interactive processes between touch and embodiment, we discuss technical solutions for specific applications, which might be used to enhance embodiment, and facilitate the study of how embodiment might alter human-robot interactions. We postulate that high-density and large surface sensing and stimulation are required to foster embodiment of such assistive devices.@en