Inductive-capacitive-inductive (LCL)-type line filters are widely used in grid-connected voltage source inverters (VSIs), since they can provide substantially improved attenuation of switching harmonics in currents injected into the grid with lower cost, weight and power losses than their L-type counterparts. However, the inclusion of third order LCL network complicates the current control design regarding the system stability issues because of an inherent resonance peak which appears in the open-loop transfer function of the inverter control system near the control stability boundary. To avoid passive (resistive) resonance damping solutions, due to their additional power losses, active damping (AD) techniques are often applied with proper control algorithms in order to damp the LCL filter resonance and stabilize the system. Among these techniques, the capacitor current feedback (CCF) AD has attracted considerable attention due to its effective damping performance and simple implementation. This paper thus presents a state-of-the-art review of resonance and stability characteristics of CCF-based AD approaches for a digitally-controlled LCL filter-based grid-connected inverter taking into account the effect of computation and pulse width modulation (PWM) delays along with a detailed analysis on proper design and implementation.