Despite our image of Earth as "the water planet," global supplies of uncontaminated surface and groundwater are indispensable, yet fragile, natural resources. Threats to freshwater supplies in the form of contamination must be understood to assure sustainable supplies, as well as to guide effective remediation and future development. However conventional models that do not account for heterogeneity (i.e. the natural variability in the geologic makeup of aquifers) are inadequate. For example, studies by the National Research Council show that court-ordered remediation strategies can fail to adequately remediate polluted sites 90% of the time. Many of these failures can be attributed to designs based on classical models that do not account for the presence of subsurface heterogeneity. To overarching goal of this work is to develop models and novel theoretical descriptions that incorporate the influence of heterogeneity. These will ultimately provide policy makers, legal authorities, stakeholders and managers with improved tools to better design and assess remediation strategies and protect current water resources.