Bayesian optimization (BO) is a powerful method for optimizing expensive, noisy black-box functions, with applications in science, engineering, economics, and manufacturing. This paper reviews recent developments in BO for designing next-generation sustainable process systems. It discusses how advanced BO methods have been developed to efficiently tackle important problems in various applications, including materials design, reaction design, process design, and control system design. BO provides a systematic and versatile way to identify highly informative design candidates using minimal function evaluations. The paper highlights the importance of improving the quality of the probabilistic model, the choice of internal optimization procedure, and the exploitation of problem structure to enhance sample efficiency. It also addresses challenges such as high-dimensional search spaces, discrete decisions, multiple objectives, and constraints. Emerging directions in BO include handling hybrid discrete-continuous search spaces, multi-objective optimization, physics-based knowledge, black-box constraints, path constraints, and multiple models or fidelities. The paper concludes with future research directions, emphasizing the need for new methods that can handle multiple challenges simultaneously and for theoretical advancements to improve BO performance. The unique challenges of sustainable process systems offer opportunities for new machine learning technologies and improvements in BO methods.Bayesian optimization (BO) is a powerful method for optimizing expensive, noisy black-box functions, with applications in science, engineering, economics, and manufacturing. This paper reviews recent developments in BO for designing next-generation sustainable process systems. It discusses how advanced BO methods have been developed to efficiently tackle important problems in various applications, including materials design, reaction design, process design, and control system design. BO provides a systematic and versatile way to identify highly informative design candidates using minimal function evaluations. The paper highlights the importance of improving the quality of the probabilistic model, the choice of internal optimization procedure, and the exploitation of problem structure to enhance sample efficiency. It also addresses challenges such as high-dimensional search spaces, discrete decisions, multiple objectives, and constraints. Emerging directions in BO include handling hybrid discrete-continuous search spaces, multi-objective optimization, physics-based knowledge, black-box constraints, path constraints, and multiple models or fidelities. The paper concludes with future research directions, emphasizing the need for new methods that can handle multiple challenges simultaneously and for theoretical advancements to improve BO performance. The unique challenges of sustainable process systems offer opportunities for new machine learning technologies and improvements in BO methods.