Robot-assisted physical therapy of the upper limb is becoming popular among the rehabilitation community. The wrist is the second most complicated joint in the upper limb after shoulder in terms of degrees of freedom. Several robotic devices have been developed during the past three decades for wrist joint rehabilitation. Intensive physical therapy and repetitive self-practice, with objective measurement of performance, could be provided by using these wrist rehabilitation robots at a low cost. There has been an increasing trend in the development of wrist rehabilitation robots to provide safe and customized therapy according to the disability level of patients. The mechanical design and control paradigms are two active fields of research undergoing rapid developments in the field of robot-assisted wrist rehabilitation. The mechanical design of these robots could be divided into the categories of end-effector based robots and wearable robotic orthoses. The control for these wrist rehabilitation robots could also be divided into the conventional trajectory tracking control mode and the assist-as-needed control mode for providing customized robotic assistance. This article presents a review of the mechanical design and control aspects of wrist rehabilitation robots. Experimental evaluations of these robots with healthy and neurologically impaired are also discussed along with the future directions of research in the design and control domains of wrist rehabilitation robots.