The hand is an organ of grasping as well as sensation, communication, and fine dexterity. Since the 80’s, many researchers have been attempting to develop robotic devices aiming at replicating the functions of the human hand in the fields of industrial robotics, tele-manipulation, humanoid robotics, and upper limb prosthetics. A special kind of robotic hand is the hand exoskeleton, that is directly attached to the human hand with the aim of providing assistance in motion/power generation. Hand exoskeletons are increasingly widespread in robot-based rehabilitation of patients suffering from different pathologies (in particular neurological diseases). This paper reviews the state-of-the-art of hand exoskeletons developed for rehabilitation purposes and proposes a new systematic classification according to three key points related to the kinematic architecture: (i) mobility of a single finger exoskeleton, (ii) number of physical connections between the exoskeleton and the human finger phalanges, and (iii) way of integration of the exoskeleton mechanism with the human parts. The discussion based upon the classification can be helpful to understand the reasons of adopting certain solutions for specific applications and the advantages and drawbacks of different designs, based on the work already done by other researchers. The final purpose of the proposed classification is then to provide guidelines useful for the design of new hand exoskeletons on the basis of a systematic analysis. As an example, the solution designed, manufactured and clinically tested by the authors is reported.