For computationally intensive tasks such as design optimization, global sensitivity analysis, or parameter estimation, a model of interest needs to be evaluated multiple times exploring potential parameter ranges or design conditions. If a single simulation of the computational model is expensive, it is common to employ a precomputed surrogate approximation instead. The construction of an appropriate surrogate does still require a number of training evaluations of the original model. Typically, more function evaluations lead to more accurate surrogates, and therefore a careful accuracy-vs-efficiency tradeoff needs to take place for a given computational task. This chapter specifically focuses on polynomial chaos surrogates that are well suited for forward uncertainty propagation tasks, discusses a few construction mechanisms for such surrogates, and demonstrates the computational gain on select test functions.