Optimal experimental design (OED) is crucial for acquiring data efficiently in scientific, engineering, and policy contexts. This article provides a systematic survey of modern OED, covering its foundations in classical design theory and current research involving complex models. It discusses criteria for formulating OED problems, emphasizing Bayesian and decision-theoretic approaches suitable for nonlinear and non-Gaussian models. The article also addresses methods for estimating or bounding design criteria, which can be challenging due to nonlinearities, high-dimensional parameters, and implicit models. Computational issues include optimization methods for finding designs, both in discrete and continuous settings. Emerging methods for sequential OED are highlighted, which adapt to experimental outcomes and coordinate experiments. The article also identifies important open questions and challenges in the field. The article begins with an introduction to OED, explaining its role in data acquisition and model improvement. It then discusses design criteria, including linear-Gaussian models, Bayesian optimality, and decision-theoretic formulations. It covers challenges in nonlinear design, where the Fisher information matrix varies with parameters, and introduces minimax and Bayesian approaches. The article also explores decision- and information-theoretic formulations, emphasizing expected information gain and mutual information as key criteria. It concludes with an outlook on future research directions and challenges in OED.Optimal experimental design (OED) is crucial for acquiring data efficiently in scientific, engineering, and policy contexts. This article provides a systematic survey of modern OED, covering its foundations in classical design theory and current research involving complex models. It discusses criteria for formulating OED problems, emphasizing Bayesian and decision-theoretic approaches suitable for nonlinear and non-Gaussian models. The article also addresses methods for estimating or bounding design criteria, which can be challenging due to nonlinearities, high-dimensional parameters, and implicit models. Computational issues include optimization methods for finding designs, both in discrete and continuous settings. Emerging methods for sequential OED are highlighted, which adapt to experimental outcomes and coordinate experiments. The article also identifies important open questions and challenges in the field. The article begins with an introduction to OED, explaining its role in data acquisition and model improvement. It then discusses design criteria, including linear-Gaussian models, Bayesian optimality, and decision-theoretic formulations. It covers challenges in nonlinear design, where the Fisher information matrix varies with parameters, and introduces minimax and Bayesian approaches. The article also explores decision- and information-theoretic formulations, emphasizing expected information gain and mutual information as key criteria. It concludes with an outlook on future research directions and challenges in OED.