Due to the dexterous manipulation capability and low metabolic energy consumption property of the human hand, many robotic hands were designed and manufactured that are inspired from the human hand. One of the technical challenges in designing biomimetic robot hands is the control scheme. The control algorithm used in a robot hand is expected to ensure the tracking of reference trajectories of fingertips and joint angles with high accuracy, reliability, and smoothness. In this chapter, trajectory-tracking performances of different types of widely used control strategies (i.e. classical, robust, and intelligent controllers) are comparatively evaluated. To accomplish this evaluation, PID, sliding mode, and fuzzy logic controllers are implemented on a biomimetic robot hand finger model and simulation results are quantitatively analyzed. Pros and cons of the corresponding control algorithms are also discussed.