Stochastic modeling has become a popular approach to quantify uncertainty in practical models.The uncertainty in the models input must be propagated through the model in order to quantify the uncertainty in the models output.The uncertainty in the models is often parametrized in a high-dimensional random space.This leads to a great challenge for the numerical simulation.High dimensional model representation(HDMR)techniques can be used to efficiently tackle the high-dimensionality and obtain a reduced model.In the talk,we present the state-of-the-art HDMR techniques for stochastic model reduction.The synergy of the HDMR techniques and numerical multiscale methods on a coarse grid can reduces the stochastic models in both stochastic space and physical space,and significantly decreases the computation complexity.A few numerical experiments are carried out to confirm the performance of these techniques.