Stochastic computation has received intensive attention in recent years, due to the pressing need to conduct uncertainty quantification (UQ) in practical computing. In this talk, we will first give an brief review of the stochastic collocation method via compressive sensing. Then we focus on the different sampling methods in collocation algorithms, including both randomized quadratues and low-discrepancy point sets. Derivative enhanced l1-minimization is also considered in this talk.