Robot-mediated neurorehabilitation is a growing field that seeks to incorporate advances in robotics combined with neuroscience and rehabilitation to define new methods for treating problems related with neurological diseases. In this paper, a systematic literature review is conducted to identify the contribution of robotics for upper limb neurorehabilitation, highlighting its relation with the rehabilitation cycle, and to clarify the prospective research directions in the development of more autonomous rehabilitation processes. With this aim, first, a study and definition of a general rehabilitation process are made, and then, it is particularized for the case of neurorehabilitation, identifying the components involved in the cycle and their degree of interaction between them. Next, this generic process is compared with the current literature in robotics focused on upper limb treatment, analyzing which components of this rehabilitation cycle are being investigated. Finally, the challenges and opportunities to obtain more autonomous rehabilitation processes are discussed. In addition, based on this study, a series of technical requirements that should be taken into account when designing and implementing autonomous robotic systems for rehabilitation is presented and discussed.