Stochastic differential equations (SDEs) play an important role in many scientific applications. It is difficult to fully understand the long-term dynamics of SDEs using rigorous approaches. Conventional numerical methods also have certain limitations. In this talk, I will review some of my recent work on data-driven computation methods for computing long-term dynamics of stochastic differential equations. This includes the computation of the invariant probability measure, the quasi-stationary distribution (QSD), and the speed of convergence towards the invariant probability measure. If time permits, I will briefly introduce some applications in sensitivity analysis and deep learning theory.