The lean blowout (LBO) limit plays a critical role in the operation of gas turbine combustors. In order to achieve the quick prediction of the LBO limit, three major prediction tools for the LBO limit, i.e. the semi-empirical correlation, the numerical prediction method and the hybrid prediction method are proposed. The semi-empirical correlations are mainly based on the characteristic time (CT) model and the perfect stirred reactor (PSR) model. The semi-empirical correlations based on the PSR model are widely applied. Among these correlations, Lefebvre's LBO model that had been validated on 8 different aero gas turbine combustors with the uncertainty ±30% is the most successful. Later, many researchers did further studies to improve Lefebvre's LBO model. The numerical prediction methods are reported increasingly with the rapid development of the computing power. Up to now, some researchers validated the numerical prediction methods in 2 different combustor configurations with the prediction uncertainties about ±25%. More studies are required to validate the effects of the combustor configurations and the atomization performances on the LBO limit. The hybrid prediction methods try to combine the semi-empirical correlations with the numerical methods and are widely attempted in recent years. Many researchers have studied the numerical based hybrid method, which needs more validations and general criterions for different configurations and operating conditions. Other researchers have studied the semi-empirical based hybrid method, which has shown good agreement for 11 different combustor configurations with the prediction uncertainties about ±16%. Further improvements are required for all prediction tools to achieve more general and accurate predictions for the LBO limits of gas turbine combustors.