Several recent studies have indicated that upper extremity injuries are classified as a top common workplace injury. Therefore, upper extremity rehabilitation has become a leading research area in the last few decades. However, this high number of upper extremity injuries is viewed as a challenging problem due to the insufficient number of physiotherapists. With the recent advancements in technology, robots have been widely involved in upper extremity rehabilitation exercises. Although robotic technology and its involvement in the rehabilitation field are rapidly evolving, the literature lacks a recent review that addresses the updates in the robotic upper extremity rehabilitation field. Thus, this paper presents a comprehensive review of state-of-the-art robotic upper extremity rehabilitation solutions, with a detailed classification of various rehabilitative robots. The paper also reports some experimental robotic trials and their outcomes in clinics.