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Moraine dams, impounding glacial lakes, are among the weak natural dams because of their slope, freeboard and composition. Glacial lake outburst floods occurring due to the failure of moraine dams are significant hazards for the valley downstream the failure, as they possess huge amount of hydraulic energy that can kill thousands and destroy infrastructures and riverine landscape. Also, the entrainment of debris to the flow from the breaching process and downstream channel may develop the flow into a much bigger disaster or even a series of hazard chain. Ice and rock avalanche or landslide, glacier calving, degradation of ice cores, earthquake and atmospheric events trigger the breaching phenomenon which generates a series of waves overtopping the dam or seepage causing the failure of the dam. Various approaches have been discussed in this review paper to produce an understanding of the failure mechanism of moraine dams: experimental works, empirical relationships, analytical solutions, and numerical modelling. No concrete experimental investigations and parametric solutions pertained to the failure mechanism of moraine dam is found in the review, but various empirical relationships are discussed and suitable approaches for numerical modelling are suggested as per the requirement of the task.