Robot-aided systems to support the physical rehabilitation of individuals with neurological impairment is one of the fields that has been widely developed in the last few decades. However, the adoption of these systems in clinical practice remains limited. In order to better understanding the causes of this limitation, a systematic review of robot-based systems focused on upper extremity rehabilitation is presented in this paper. A systematic search and review of related articles in the literature were conducted. The chosen works were analyzed according to the type of device, the data analysis capability, the therapy method, the human–robot interaction, the safety strategies, and the focus of treatment. As a conclusion, self-adaptation for personalizing the treatments, safeguarding and enhancing of patient–robot interaction towards training essential factors of movement generation into the same paradigm, or the use of lifelike environments in fully-immersive virtual reality for increasing the assimilation of motor gains could be relevant factors to develop more accepted robot-aided systems in clinical practice.