When detecting the presence of partial discharge (PD) activity in the insulation system in high-voltage equipment, the excitation voltages at variable frequency have been widely used instead of power-frequency (50/60 Hz) sinusoidal voltage in order to reduce the charging power. This work reviews the relevant research on PD activity at very low frequency (VLF) method, including sinusoidal or cosine-rectangular voltage shape, and damped AC (DAC) method. Based on the research history and development status, some major PD characteristics, such as PD inception voltage (PDIV), PD amplitude, PD charge, PD phase-resolved pattern, and several hot issues, such as surface charge decay and statistical time lag, have been discussed. Moreover, the advantages, disadvantages, and applied conditions of two reviewed methods has been summarized. Finally, the prospects have been made on the main development trends of this research field in the future.@en