Sensory perception for dexterous robotic hands is an active research area and recent progress in robotics. Effective dexterous manipulation requires robotic hands to accurately feedback their state or perceive the surrounding environment. This article reviews the state-of-the-art of sensory perception for dexterous robotic manipulation. Two types of sensors, such as intrinsic and extrinsic sensors, are introduced according to their function and layout in robotic hands. These sensors provide rich information to a robotic hand, which contains the posture, the contact information of objects, and the physical information of the environment. Then, a comprehensive analysis of perception methods including planning-level, control-level, and learning-level perceptions is presented. The information obtained from sensory perception can help robotic hands to make decisions effectively. Previously issued reviews mainly focus on the design of tactile senor, while we analyze and discuss the relationship among sensing, perception, and dexterous manipulation. Some potential research topics on sensory perception are also summarized and discussed.