Micromanipulation is a hot topic due to its enabling role in various research fields. In order to perform a high precision operation at a small scale, compliant mechanisms have been proposed and applied for decades. In microscale manipulation, micro-/nano-positioning is the most fundamental operation because a precision positioning is the premise of subsequent operations. This paper is concentrated on reviewing the state-of-the-art research on complaint micro-/nano-positioning stage design in recent years. It involves the major processes and components for designing a compliant positioning stage, e.g., actuator selection, stroke amplifier design, connecting scheme of the multi-DOF stage and structure optimization. The review provides a reference to design a compliant micro-/nano-positioning stage for pertinent applications.