The active power-decoupling (APD) method is an effective solution to handle the inherent double-line frequency ripple power in single-phase power systems. It removes the bulky passive devices and facilitates the improvement of the system power density and even the reliability. This article provides a comprehensive review of the prior-art and state-of-the-art control strategies in APD. They are categorized into four groups according to the basic control ideas of “power balance,” “harmonic suppression,” “volt-second balance/charge balance,” and “virtual impedance.” And the specific control strategies under each control idea are discussed and compared. The pros and cons of each control idea are also presented . Finally, this article draws a sketch of the global trends in APD control.