This paper gives an overview of computationally efficient stochastic response surface techniques based on non-intrusive polynomial chaos (NIPC) for uncertainty quantification in numerical models. The results of uncertainty analysis can be used in robust and reliability-based design and optimisation studies as well as the assessment of the accuracy of the simulation results. In particular, the uncertainty quantification with NIPC methods which require no modification to the existing deterministic models are demonstrated on computational fluid dynamics (CFD) simulations in this paper. The NIPC methods have been increasingly used for uncertainty propagation in high-fidelity CFD simulations due to their non-intrusive nature and strong potential for addressing the computational efficiency and accuracy requirements associated with large-scale complex stochastic simulations. The theory and description of various NIPC methods used for non-deterministic CFD simulations are presented, which can be applied to any other computational models used in analysis and optimisation problems. Several stochastic fluid dynamics examples are given to demonstrate the application and effectiveness of NIPC methods for uncertainty quantification in fluid dynamics. These examples include stochastic computational analysis of a laminar boundary layer flow over a flat plate, supersonic expansion wave problem, and inviscid transonic flow over a three-dimensional wing with rigid and aeroelastic assumptions.