Solving inverse problems for nonlinear simulation models with nonlinear objective is usually a global optimization problem. This talk will present an overview of the development of algorithms that employ response surfaces as a surrogate for an expensive simulation model to significantly reduce the computational effort required to solve continuous global optimization problems and uncertainty analysis of simulation models that require a substantial amount of CPU time for each simulation. I will show that for many cases of nonlinear simulation models, the resulting optimization problem is multimodal and hence requires a global optimization method. In order to reduce the number of simulations required, we are interested in utilizing information from all previous simulations done as part of an optimization search by building a (radial basis function) multivariate response surface that interpolates these earlier simulations. I will discuss the alternative approaches of direct global optimization search versus using a multistart method in combination with a local optimization method. I will also describe an uncertainty analysis method SOARS that uses derivative-free optimization to help construct a response surface of the likelihood function to which Markov Chain Monte Carlo is applied. This approach has been shown to reduce CPU requirements to less than 1/65 of what is required by conventional MCMC uncertainty analysis. I will present examples of the application of these methods to significant environmental problems described by computationally intensive simulation models used worldwide. One model (TOUGH2) involves partial differential equation models for fluid flow for carbon sequestration and the second is SWAT, which is used to describe potential pollution of NYC’s drinking water. In both cases, the model uses site-specific data. This work has been a collaboration with others including: R. Regis and Y. Wang (Optimization), N. Bliznyuk and D. Ruppert (uncertainty), A. Espinet and J. Woodbury (Environmental Applications)