The scales of concern in subsurface transport of contaminants from low-level radioactive waste disposal facilities are in the range of 1 to 1,000 m. Natural geologic materials generally show very substantial spatial variability in hydraulic properties over this range of scales. Such heterogeneity can significantly influence the migration of contaminants. It is also envisioned that complex earth structures will be constructed to isolate the waste and minimize infiltration of water into the facility. The flow of water and gases through such facilities must also be a concern. A stochastic theory describing unsaturated flow and contamination transport in naturally heterogeneous soils has been enhanced by adopting a more realistic characterization of soil variability. The enhanced theory is used to predict field-scale effective properties and variances of tension and moisture content. Applications illustrate the important effects of small-scale heterogeneity on large-scale anisotropy and hysteresis and demonstrate the feasibility of simulating two-dimensional flow systems at time and space scales of interest in radioactive waste disposal investigations. Numerical algorithms for predicting field scale unsaturated flow and contaminant transport have been improved by requiring them to respect fundamental physical principles such as mass conservation. These algorithms are able to provide realistic simulations of systems with very dry initial conditions and high degrees of heterogeneity. Numerical simulation of the movement of water and air in unsaturated soils has demonstrated the importance of air pathways for contaminant transport. The stochastic flow and transport theory has been used to develop a systematic approach to performance assessment and site characterization. Hypothesis-testing techniques have been used to determine whether model predictions are consistent with observed data.