Grid-connected inverters are key components of distributed generation systems (DGSs) and micro-grids (MGs), because they are effective interfaces for renewable and sustainable distributed energy resources (DERs). Recently, multi-functional grid-connected inverters (MFGCIs) have attracted more and more attention for their benefits on auxiliary services on power quality enhancement in DGSs and MGs. These kinds of converters can not only achieve the power generation of DERs, but also can perform as power quality conditioners at their grid-connected points. It should be noted that these functionalities are optimally organized in the same device, which can significantly enhance the cost-effective feature of the grid-connected inverter, as well as can decrease the investment and bulk compared with multiple devices with independent functionalities. MFGCIs are especially suitable for DGSs and MGs application due to their good performances and benefits. Topologies and control strategies of MFGCIs are comprehensively reviewed in this paper. Additionally, detailed explanation, comparison, and discussion on MFGCIs are achieved. Furthermore, some future research fields on MFGCIs are well summarized.