The topic of this talk deals with the derivation of a posteriori error estimators for the control of approximation and modeling errors with respect to quantities of interest. The methodology is based on the notion of the adjoint problem of linear initial- and boundary-value problems and can be viewed as a generalization of the concept of Green’s function for the case of point-wise quantities. Post-processing of the error estimates provide refinement indicators for model or mesh adaptation in order to control errors in quantities of interest. The talk will present an extension to nonlinear boundary-value problems and quantities of interest, in which case the errors consist of a contribution involving the residual and the solution of a linearized adjoint problem, and a contribution combining higher-order terms that characterize the linearization error. Although the linearization error contribution is usually neglected, we will show that nonlinear effects may, in some cases, be significant and should perhaps be accounted for. We will then present applications of the goal-oriented error estimation methodology to adaptive modeling, starting from a hierarchy of models that can describe a given physical phenomenon, and to the development of surrogate models for response surfaces, which can be efficiently utilized to estimate the parameters of Reynolds-averaged Navier-Stokes models.