Abstract: Flow of freshwater and saltwater intrusion in coastal aquifers has drawn the attention of many investigators. Several laboratory, as well as mathematical models have been developed to study the pattern of flow of groundwater in coastal aquifers. Mathematical models have wider range of application and are the concern of this paper. Due to the complex nature of the problem, each of these mathematical models are based on certain simplifying assumptions and approximations. This paper presents a critical review of various methods of solution which have been proposed. The validity of the results abtained and the limitations of these models are also discussed.