Wind energy is rapidly growing in recent years. Among different types of wind turbines, due to several advantages, permanent magnet synchronous generator (PMSG) is attractive concept. Since the penetration level of wind power in the grid is increased, therefore, wind power can influence to the grid and vice versa. Some of the important problems in the grid are fault condition and voltage sags. These conditions may affect the operation of wind turbine. In order to enhance low voltage ride through (LVRT) capability in PMSG-based wind turbines, various approaches have been proposed in the last years. In this paper, the review and comparison of several LVRT capability enhancement methods is performed. The two foremost types of LVRT capability enhancement methods are external devices based methods and modified controller based methods. The main objectives of this paper are to introduce performances of different LVRT capability enhancement methods and use of some LVRT capability enhancement methods in PMSG based wind turbine which are applied in other kind of wind power generators. The external devices based methods can be effective but some of these methods are of significant cost. According to the literatures, modified controller based methods can reduce the LVRT capability enhancement cost. Several modified controller based methods have been proposed for LVRT capability enhancement. To compare the mentioned methods, several simulations are performed in MATLAB software. From the review of simulation results, series connection of FACTS devices and modification of back-to-back converter controllers are the highly efficient LVRT capability enhancement approaches.