Single-phase power converters are widely used in electric distribution systems under 10 kilowatts, where the second-order power imbalance between the AC side and DC side is an inherent issue. The pulsating power is decoupled from the desired constant DC power, through an auxiliary circuit using energy storage components. This paper provides a comprehensive overview of the evolution of single-phase converter topologies underlining power decoupling techniques. Passive power decoupling techniques were commonly used in single-phase power converters before active power decoupling techniques were developed. Since then, active power decoupling topologies have generally evolved based on three streams of concepts: 1) current-reference active power decoupling; 2) DC voltage-reference active power decoupling; and 3) AC voltage-reference active power decoupling. The benefits and drawbacks of each topology have been presented and compared with its predecessor, revealing underlying logic in the evolution of the topologies. In addition, a general comparison has also been made in terms of decoupling capacitance/inductance, additional cost, efficiency and complexity of control, providing a benchmark for future power decoupling topologies.