Many of the parameters in subsurface flow and transport models cannot be estimated directly at the scale of interest, but can only be derived through inverse modeling. During this process, the parameters are adjusted in such a way that the behavior of the model approximates, as closely and consistently as possible, the observed response of the system under study for some historical period of time. We briefly review the current state of the art of inverse modeling for estimating unsaturated flow and transport processes. We summariz how the inverse method works, discuss the historical background that led to the current perspectives on inverse modeling, and review the solution algorithms used to solve the parameter estimation problem. We then highlight our recent work at Los Alamos related to the development and implementation of improved optimization and data assimilation methods for computationally efficient calibration and uncertainty estimation in complex, distributed flow and transport models using parallel computing capabilities. Finally, we illustrate these developments with three different case studies, including (i) the calibration of a fully coupled three-dimensional vapor extraction model using measured concentrations of volatile organic compounds in the subsurface near the Los Alamos National Laboratory, (ii) the multiobjective inverse estimation of soil hydraulic properties in the HYDRUS-1D model using observed tensiometric data from an experimental field plot in New Zealand, and (iii) the simultaneous estimation of parameter and states in a groundwater solute mixture model using data from a multitracer experiment at Yucca Mountain, Nevada.

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