Optimal transport projections have found various applications in areas such as operations research (e.g. distributionally robust optimization); statistics (e.g. hypothesis testing and causal inference), and algorithm evaluation (e.g. fairness and stability), among others. We will summarize some of these applications and interpret the projection and associated statistics in these applied settings. Moreover, we will discuss the advantages of optimal transport projections for some of fundamental statistical tasks such as hypothesis testing in comparison to other mainstream approaches, such as empirical likelihood. We will finish the discussion by introducing non-linear projections and their applications to distributionally robust Bayesian control for Merton’s problem and associated challenges.