Abstract: The grid-tied inverter, which serves as a key interface that connects the renewable-energy-based distributed power generation and the grid, plays a major role in feeding electrical energy into the power grid with high efficiency and quality. However, with the increasing penetration rate of renewable energies, the point of common coupling of the inverter suffers complex grid conditions such as large grid impedance, rich background harmonics, grid voltage fluctuations, frequency derivation or even grid faults. In view of the fact that the grid-tied inverter is essentially a nonlinear system with multiple inputs and strong coupling, it is difficult to explain the complex harmonic oscillation phenomenon using the traditional linear modeling and stability analysis methods, which poses great challenges to the stability analysis and stable operation of the grid-tied inverter. Therefore, this paper first clarifies the relationship between nonlinearity and large-disturbance stability, indicating that the large-signal stability analysis depends more on the application of nonlinear modeling and analysis methods. On this basis, several reported nonlinear stability analysis methods in grid-tied inverters are summarized and compared. Furthermore, the application of stability analysis methods with respect to specific nonlinear factors in grid-tied inverters is elaborated. Finally, the limitations of the existing studies are discussed in order to further promote the research on nonlinear modeling and stability analysis of grid-tied inverters in "double high" power systems.