The objective of this research is to develop methods of predicting large-scale contaminant transport processes in naturally heterogeneous aquifers. The aquifer heterogeneity is represented by a three-dimensional random field and the resulting transport processes are predicted by using a small perturbation spectral representation technique to solve the governing stochastic differential equations. The validity and limitations of the theoretical results are evaluated using large- scale three-dimensional numerical simulations employing state of the art supercomputer facilities. The theoretical results will also be compared with ongoing field experiments. Using these techniques, the research specifically addresses unresolved issues regarding highly heterogeneous aquifers, unsteady flow effects, non-stationarity heterogeneous reactive processes and two-phase flow. This research is expected to establish methods of predicting field-scale transport parameters from small-scale laboratory or field measurements. Quantitative predictions of these field- scale transport processes are a central element of schemes to regulate and rectify groundwater contamination associated with waste disposal activities. The research will also be of broad scientific interest in that it will establish systematic methods of predicting the large-scale behavior of complex, naturally heterogeneous environmental systems.