Multifingered robotic hands (usually referred to as dexterous hands) are designed to achieve human-level or human-like manipulations for robots or as prostheses for the disabled. The research dates back 30 years ago, yet, there remain great challenges to effectively design and control them due to their high dimensionality of configuration, frequently switched interaction modes, and various task generalization requirements. This article aims to give a brief overview of multifingered robotic manipulation from three aspects: a) the biological results, b) the structural evolvements, and c) the learning methods, and discuss potential future directions. First, we investigate the structure and principle of hand-centered visual sensing, tactile sensing, and motor control and related behavioral results. Then, we review several typical multifingered dexterous hands from task scenarios, actuation mechanisms, and in-hand sensors points. Third, we report the recent progress of various learning-based multifingered manipulation methods, including but not limited to reinforcement learning, imitation learning, and other sub-class methods. The article concludes with open issues and our thoughts on future directions.