The article provides a comprehensive survey of optimal experimental design (OED), covering both formulations and computational methods. OED aims to optimize the acquisition of data for modeling and prediction in various fields, including natural sciences, engineering, and policy making. The authors review the criteria used to formulate OED problems, emphasizing the flexibility of Bayesian and decision-theoretic approaches, which are well-suited for nonlinear and non-Gaussian statistical models. They discuss methods for estimating or bounding design criteria, which can be challenging due to strong nonlinearities, high-dimensional parameters, and large per-sample costs. The article also covers optimization methods for finding designs, including discrete and continuous settings, and presents emerging methods for sequential OED, which adapt to the outcomes of past experiments. The authors highlight open questions and challenges in the field, making it a valuable resource for researchers and practitioners in OED.The article provides a comprehensive survey of optimal experimental design (OED), covering both formulations and computational methods. OED aims to optimize the acquisition of data for modeling and prediction in various fields, including natural sciences, engineering, and policy making. The authors review the criteria used to formulate OED problems, emphasizing the flexibility of Bayesian and decision-theoretic approaches, which are well-suited for nonlinear and non-Gaussian statistical models. They discuss methods for estimating or bounding design criteria, which can be challenging due to strong nonlinearities, high-dimensional parameters, and large per-sample costs. The article also covers optimization methods for finding designs, including discrete and continuous settings, and presents emerging methods for sequential OED, which adapt to the outcomes of past experiments. The authors highlight open questions and challenges in the field, making it a valuable resource for researchers and practitioners in OED.