Abstract: The studies on numerical simulation of contaminant transport and flow in North China type fracture-karst media last decades are reviewed,the numerical methods and computational techniques which have been developed to solve problems of contaminant transport and flow are examined.The key and well-noticed problems in connection with the numerical simulation, which include parameter identification and scale effect,numerical dispersion and libration,non-Darcy flow and Non-Fickian transport,study of stochastic methods,and so on,are highlighted.Attempts have been made to compare and contrast representative numerical methods,and the direction for future research is suggested.