This chapter presents the subset simulation (SS) approach and the Polynomial Cha-os Expansion (PCE) methodology. The SS method is an efficient alternative to the well-known Monte Carlo Simulation (MCS) methodology to calculate small failure probabilities. The basic idea of the SS approach is that the small failure probability can be expressed as a product of larger conditional failure probabilities. On the other hand, the PCE methodology allows one to accurately compute the PDF of a given system response using a reduced number of calls of the deterministic model (as compared to the classical MCS applied on the original complex deterministic model). Indeed, the PCE methodology replaces the computationally-expensive de-terministic model by a meta-model. Once the meta-model is determined, MCS can be applied on the obtained PCE to compute the PDF of the system response with a quasi-negligible computation time.