Currently, the stability of LCL-type grid-connected converters in distributed power generation systems (DPGS) has been numerously investigated. Resonance of high-order filters can cause system oscillations and grid current distortion. This phenomenon is more critical when the DPGS contains capacitive loads and cables. We should consider the interaction effect between the equivalent grid impedance and the converter impedance, for which many innovative passivity methods have been proposed. This digest reviews these contributions and classifies the different current controls as single-loop and multi-loop. Based on the concept of passivity, all passivity methods can guarantee the stability of the system by reshaping the output impedance, then recommend methods for different grid impedances. These methods are also evaluated and compared, finally suggestions for implementing passivity and future trends are presented.