In this paper we describe our gradient and Hessian enhanced Kriging surrogate model with dynamic sample point selection. We demonstrate the quality of the surrogate by comparison with higher-dimensional analytic test functions. We also apply the surrogate model to uncertainty quantification and robust optimization problems using inexpensive Monte-Carlo simulations. All applications benefit from the additional gradient and Hessian information as well as the dynamic sample point selection by requiring fewer function evaluations and overall less computational time.