The focus of this research is large-scale contaminant spreading in aquifers that exhibit significant variations in properties that influence groundwater flow and pollutant transport. It is widely accepted that spatial changes in hydraulic conductivity play a major role in contaminant spreading. The main goal of the study is to apply novel mathematical solutions, powerful numerical models, and visualization tools to examine and quantify the influence of spatial variations in hydraulic conductivity on contaminant spreading in highly heterogeneous aquifers. Existing mathematical models of contaminant spreading can only be applied to aquifers that exhibit small variations in hydraulic conductivity. Existing numerical models can not be used to simulate large-scale three-dimensional contaminant spreading in highly heterogeneous aquifers. The key element of the present study is a new structural model of hydraulic conductivity, introduced by Gedeon Dagan that contains isolated inclusions and a homogeneous background. Hydraulic conductivity of each inclusion is constant. Actual statistical structure of hydraulic conductivity is reproduced by varying locations, sizes, and conductivities of inclusions. Both approximate analytic models and highly precise numerical models are developed based on this new structure. Analytic and numerical models are used in this study to predict rates of contaminant spreading in highly heterogeneous aquifers. Inability to visualize three-dimensional flow and transport is a bottleneck that prevents better understanding of many three-dimensional transport phenomena. A new visualization tool, designed for immersive virtual-reality facilities, will be developed and used to investigate transport phenomena such as transverse dispersion, contaminant tailing, preferential flow and molecular diffusion. The visualization tool will include the ability to interact with a simulation in real time. A user will be able to stop the simulation of contaminant spreading and get specific data associated with any part of the model. For example, it will be possible to choose a location in the three-dimensional medium, to introduce a contaminant particle at that location, and to follow the particle throughout the aquifer with a "camera" mounted on the particle. A web-based interface will also be developed to enhance research by facilitating interactions amongst scientists in different geographical locations and to integrate research and teaching. Development and application of these models and visualization tools, termed "Virtual Porous Medium", will likely increase our ability to understand and predict contaminant spreading in aquifers. In addition, this first version of the Virtual Porous Medium will serve as a platform where other transport mechanisms (such as reactive transport) may be implemented at a later stage.