The journey of a prosthetic user is characterized by the opportunities and the limitations of a device that should enable activities of daily living (ADL). In particular, experiencing a bionic hand as a functional (and, advantageously, embodied) limb constitutes the premise for promoting the practice in using the device, mitigating the risk of its abandonment. In order to achieve such a result, different aspects need to be considered for making the artificial limb an effective solution to accomplish activities of daily living. According to such a perspective, this review aims at presenting the current issues and at envisioning the upcoming breakthroughs in upper limb prosthetic devices. We first define the sources of input and feedback involved in the system control (at user-level and device-level), alongside the related algorithms used in signal analysis. Moreover, the paper focuses on the user-centered design challenges and strategies that guide the implementation of novel solutions in this area in terms of technology acceptance, embodiment, and, in general, human-machine integration based on co-adaptive processes. We here provide the readers (belonging to the target communities of researchers, designers, developers, clinicians, industrial stakeholders, and end-users) with an overview of the state-of-the-art and the potential innovations in bionic hands features, hopefully promoting interdisciplinary efforts for solving current issues of ULPs. The integration of different perspectives should be the premise to a transdisciplinary intertwining leading to a truly holistic comprehension and improvement of the bionic hands design. Overall, this paper aims to move the boundaries in prosthetic innovation beyond the development of a tool and towards the engineering of human-centered artificial limbs.