In recent years, the wind energy conversion system faces significant challenges for stable and secure operations, especially in the weak grid due to high penetration of wind energy into the grid. Doubly fed induction generator (DFIG) is one of the most popular wind turbine generators due to its cost‐effective variable speed and low‐cost partial size power converter. Impedance interaction between series or parallel compensated weak grid and the DFIG system causes sub‐synchronous resonance (SSR) and high‐frequency resonance (HFR). A comprehensive review of the state‐of‐the‐art SSR and HFR in the DFIG system under a weak grid is presented. First, based on features, such as supplementary hardware, linear and non‐linear control strategies, the resonance damping techniques are classified into different types. Then, the advantages and disadvantages of SSR analysis and damping techniques techniques are put forward. Moreover, the latest development of state‐of‐the‐art SSR and HFR analysis and damping techniques are supplemented. Finally, the contemporary and future trends of the SSR and HFR techniques are discussed.