In this paper, gradient/Hessian-enhanced surrogate models have been developed based on Kriging approaches. The gradient/Hessian-enhanced Kriging methods have been developed based on direct and indirect formulations. The efficiencies of these methods are compared by analytical function fitting, aerodynamic data modeling and 2D airfoil drag minimization problems. For the aerodynamic problems, efficient CFD gradient/Hessian calculation methods are utilized that make use of adjoint and automatic differentiation techniques. The gradient/Hessian-enhanced surrogate models are shown to be useful in the development of efficient design optimization, aerodynamic database construction, and uncertainty analysis.