This book is one of the earliest effort in development of contaminant transport modelling in porous media which has been the focus of many researches in hydrology, soil science and environmental and Geo-environmental engineering for many years. Researches mostly have been done from the 1950s and 1960s, created the basis of theoretical developments and analyses for the classical advection-dispersion equation (ADE). Classical advection-dispersion equation can be a satisfactory transport model in homogeneous porous media under some conditions, but It is well proven that such homogeneity rarely, if ever, exists. Wide range of heterogeneity of natural porous media necessitates development of more sophisticated transport theories. The purpose of the present study is to compare analytic solution of ADE with two effective numerical and stochastic models based on finite difference and continuous time random walk to determine the most reliable and accurate method for contaminant transport modeling with focusing on transport of contaminant in heterogeneous porous media.