In this paper, we are interested in the numerical approximations of a transformation u of a set of independent random variables X = (X1, ..., XQ) t ∈ R^Q into an output one u(X) ∈ R thanks to generalized Polynomial Chaos (gPC) based methods. In particular, we aim at recalling the main results on the methods, their constructions, analysis and comparisons. Amongst the many derivations of gPC, one can count integration-gPC, regression-gPC, collocation-gPC and even recently kriging-gPC. Although the previous different methods have been compared numerically on several benchmarks in many papers, it is still hard identifying which method performs better than the other and in which conditions. The aim of this paper is to identify more easily under which conditions the strategies differ, are equivalent or are more efficient.