Our interaction with the world rests on the knowledge that we are a body in space and time, which can interact with the environment. This awareness is usually referred to as sense of embodiment. For the good part of the past 30 years, the rubber hand illusion (RHI) has been a prime tool to study embodiment in healthy and people with a variety of clinical conditions. In this paper, we provide a critical overview of this research with a focus on the RHI paradigm as a tool to study prothesis embodiment in individuals with amputation. The RHI relies on well-documented multisensory integration mechanisms based on sensory precision, where parietal areas are involved in resolving the visuo-tactile conflict, and premotor areas in updating the conscious bodily representation. This mechanism may be transferable to prosthesis ownership in amputees. We discuss how these results might transfer to technological development of sensorised prostheses, which in turn might progress the acceptability by users.