In this paper, we present a comprehensive review of hand exoskeleton technologies for rehabilitation and assistive engineering, from basic hand biomechanics to actuator technologies. Because of rapid advances in mechanical designs and control algorithms for electro-mechanical systems, exoskeleton devices have been developed significantly, but are still limited to use in larger body areas such as upper and lower limbs. However, because of their requirements for smaller size and rich tactile sensing capabilities, hand exoskeletons still face many challenges in many technical areas, including hand biomechanics, neurophysiology, rehabilitation, actuators and sensors, physical human-robot interactions and ergonomics. This paper reviews the state-of-the-art of active hand exoskeletons for applications in the areas of rehabilitation and assistive robotics. The main requirements of these hand exoskeleton devices are also identified and the mechanical designs of existing devices are classified. The challenges facing an active hand exoskeleton robot are also discussed.