Abstract: In order to achieve the "3060" target of carbon peak and carbon neutrality, wind power will play an important role in our nation's energy system. The wake of a wind turbine is a key factor that affects the performance and levelized cost of wind power. It needs to be fully considered in the layout and control design of the wind turbine. This article first introduces the computational methods of wind turbine wakes, including analytical models, low-order models, large-eddy simulation, and methods for generating inflow turbulence. Analytical models and low-order models can compute wind turbine wakes fast, but they rely on model parameters and cannot or cannot accurately predict the turbulence characteristics of wind turbine wakes. Large-eddy simulation with parameterized models for wind turbines can accurately predict turbulence characteristics such as wake meandering. It is a powerful tool for investigating wake mechanism and can provide data and theoretical support for development of fast prediction models. Next, the article introduces the tip vortices, hub vortex and wake meandering and discusses their mechanism. For turbulent inflows, tip vortices mainly exist in the near wake. Meandering is the main feature of the far wake, which affects the characteristics of inflow for downstream wind turbines. There are two mechanisms for wake meandering: large-scale eddies of the incoming flow and shear layer instability. Numerical and observation results show that the two mechanisms coexist. The nacelle and the hub vortex have an important influence on wake meandering. Using the actuation surface model of the blade and the nacelle can accurately predict wake meandering. Research has shown that the turbulence characteristics for different designs of wind turbines are similar, which provides a theoretical basis for the development of a fast prediction model for wake turbulence. Current research efforts have been focused on wind turbine wakes on flat terrain. The mechanism of the atmospheric turbulence and wind turbine wake in complex terrain and marine environments are complex, which cannot be accurately predicted using the existing engineering models and needs further in-depth research.