Hand movement disorders caused by neurological diseases like brachial plexus injuries significantly impact daily activities of patients. Compared with the upper-limb rehabilitation that is focused on the large movements of joints, the rehabilitation of the hand movements that are dexterous remains challenging due to its exceptional flexibility. This article aims to reviewing the latest research on the system and related strategies for hand movement rehabilitation. Firstly, the development on the cutting-edge sensing technologies, actuator-driven rehabilitation equipment and hand movement pattern recognition algorithms, all contributing to the design of the hand movement rehabilitation system, are introduced. Secondly, the various rehabilitation strategies, including the active rehabilitation, passive rehabilitation, and guided rehabilitation that are tailored for patients with different disability levels at varying rehabilitation stages, are reviewed. Furthermore, the limitations of current methods and techniques are discussed and future research directions are put forward.