This paper reviews the theory and methodology for optimizing under uncertainty, a critical issue in various fields such as production planning, scheduling, location, transportation, finance, and engineering design. The author discusses classical recourse-based stochastic programming, robust stochastic programming, probabilistic (chance-constraint) programming, fuzzy programming, and stochastic dynamic programming. Each approach is evaluated based on its advantages and shortcomings, with examples provided to illustrate their applications. The paper also reviews the state-of-the-art in computations, including the use of sampling-based methods and decomposition techniques for solving large-scale problems. Additionally, it highlights recent developments in the process systems engineering community, such as flexibility analysis, aggregation-disaggregation algorithms, and multiparametric programming approaches. Finally, the paper identifies future research areas, including the development of polynomial-time approximation schemes for multi-stage stochastic programs and the application of global optimization algorithms to two-stage and chance-constraint formulations.This paper reviews the theory and methodology for optimizing under uncertainty, a critical issue in various fields such as production planning, scheduling, location, transportation, finance, and engineering design. The author discusses classical recourse-based stochastic programming, robust stochastic programming, probabilistic (chance-constraint) programming, fuzzy programming, and stochastic dynamic programming. Each approach is evaluated based on its advantages and shortcomings, with examples provided to illustrate their applications. The paper also reviews the state-of-the-art in computations, including the use of sampling-based methods and decomposition techniques for solving large-scale problems. Additionally, it highlights recent developments in the process systems engineering community, such as flexibility analysis, aggregation-disaggregation algorithms, and multiparametric programming approaches. Finally, the paper identifies future research areas, including the development of polynomial-time approximation schemes for multi-stage stochastic programs and the application of global optimization algorithms to two-stage and chance-constraint formulations.