In this paper, a universal state-space approach to uncalibrated model-free visual servoing is proposed and analyzed in detail. After an updated review of the problem, the current research development is transformed and categorized into three important schemes: Broyden–Gauss–Newton method in state space, Broyden recursive least squares method in state space, and Kalman–Bucy filter method, which are compared and investigated comprehensively. A Broyden population partition method in state space, or BP-SS-20-P, is proposed and experimentally verified as the best one at tracking fast and complicated target maneuver among those enlisted in this comparative study. Besides, a robustness theorem of uncalibrated model-free visual servoing algorithms is proposed. The state-space approach of uncalibrated model-free visual servoing provides a unified perspective, a standardized platform and much more flexibility for future work and improvement.