With the large-scale development and utilization of renewable energy, storage and flexible transmission technologies, there are more and more grid-tied inverter power generation systems in the power grid. The low inertia and weak damping characteristics of grid-tied inverters lead to the relative reduction of the rotational inertia of the traditional power grid, and the safe and stable operation ability of the power grid is also reduced. The common stability analysis methods for grid-tied inverter systems mainly include the numerical simulation methods based on differential-difference-algebraic model, the time-domain analysis methods based on state space model, and the frequency domain analysis methods based on impedance model. This paper respectively summarizes the basic principles, main features and best application scenarios of the existing analysis methods, and points out some problems in the application. Meanwhile, this paper also introduces some new stability analysis methods such as amplitude phase dynamics analysis method, static synchronous generator model and large signal stability analysis method. Finally, this paper points out that the advantages and disadvantages of various methods and their best application scenarios should be fully considered in the practical application, the dynamic characteristics and stability of grid-connected inverter power generation system should be analyzed based on a combination of various typical analysis methods and a comprehensive understanding from different perspectives.