Abstract: As the penetration rate of renewable energy sources(represented by photovoltaic and wind power)continues to increase, the characteristics of the power grid become increasingly complex. Traditional single-mode grid-following and grid-forming converters cannot fully meet the needs of power grids. Consequently, on one hand, under high penetration conditions, the problem of significant fluctuations in the impedance of local grids becomes more pronounced, exhibiting characteristics of strong to weak variations. The existing stability control of grid-connected converters still has application limitations. How to combine both control modes to ensure that the converters could compromise both economy and stability is a research hotspot. On the other hand, the control of existing grid-connected inverters is hard to adapt to the nonlinear changes in the complex grid characteristics. Under high penetration conditions, influenced by the intermittency of renewable energy sources and grid faults leading to equipment or grid branch disconnections, the structure or parameters of the grid exhibit nonlinear changes. Therefore, exploring the application of nonlinear control in grid-following and grid-forming inverters to enhance their stability under complex grid conditions is of significant importance. In summary, we reviews several control methods that combine the advantages of both grid-following and grid-forming modes, based on the single-mode control of grid-forming and grid-following converters. These methods include single-converter dual-mode switching control, single-converter dual-mode integrated control, and multi-converters station hybrid mode control. Furthermore, this paper elaborates how to improve the existing control of grid-connected inverters to adapt to the nonlinear changes in complex grid characteristics. Finally, we provide an outlook on future control technologies of converters.