The two-stage stochastic variational inequality (SVI) provides a powerful modeling paradigm for many important applications in which uncertainties and equilibrium are present. The two-stage SVI is to find a pair: here-and-now solution and wait-and-see solution. The here-and-now solution represents now-decisions, while the wait-and-see solution depends on future events described by random variables. This talk reviews some new theory and algorithms for the two-stage SVI. Moreover, we formulate a convex two-stage non-cooperative multi-agent game under uncertainty as a two-stage SVI. Numerical results based on historical data in crude oil market are presented to demonstrate the effectiveness of the two-stage SVI in describing the market share of oil producing agents.