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Using limited observation data of groundwater quality, models of groundwater pollution source identification can be used to estimate the locations, leakage rate, and the dominant processes of the pollution sources, which thus can provide a reference for formulating remedial schemes for groundwater pollution. Based on the principles and theories of pollutant movement and source identification, this paper presents an overview of existing mathematical methods, including direct methods (inverse particle tracing methods and regularization-based methods) and indirect methods (optimization-based and probability-based methods). The main problems in the application of these methods are (1) the complexity of groundwater pollution source identification, (2) groundwater organic contamination, and (3) the low efficiency of model calculation. Integrated research of soil-groundwater systems, instrumentation-based groundwater pollution monitoring, identification of NAPL pollutants, and GPU-based heterogeneous parallel computing will be the keys to groundwater pollution source identification in the future. [ABSTRACT FROM AUTHOR]