In this paper, several formulations for optimization under uncertainty are presented. In addition to the direct nesting of uncertainty quantification within optimization, formulations are presented for surrogate-based optimization under uncertainty in which the surrogate model appears at the optimization level, at the uncertainty quantification level, or at both levels. These surrogate models encompass both data fit and hierarchical surrogates. The DAKOTA software framework is used to provide the foundation for prototyping and initial benchmarking of these formulations. A critical component is the extension of algorithmic techniques for deterministic surrogate-based optimization to these surrogate-based optimization under uncertainty formulations. This involves the use of sequential trust regionbased approaches to manage the extent of the approximations and verify the approximate optima. Two analytic test problems and one engineering problem are solved using the different methodologies in order to compare their relative merits. Results show that surrogate-based optimization under uncertainty formulations show promise both in reducing the number of function evaluations required and in mitigating the effects of nonsmooth response variations.