Dynamic Traffic Assignment (DTA) has evolved significantly since its pioneering work by Merchant and Nemhauser. This special issue aims to document the main existing DTA approaches for future reference. The paper provides an overview of the current understanding of DTA, reviews the existing literature, connects it to the approaches presented in the special issue, and hypothesizes about the future. DTA refers to a broad spectrum of problems, each with different decision variables, behavioral assumptions, and data requirements. The general DTA problem is characterized by ill-behaved system properties due to time-varying flows and randomness in system inputs. This complexity has led to a dichotomy of approaches, ranging from analytical to simulation-based methods. Despite the theoretical intractability, practical solutions have been developed that are effective and efficient for realistic scenarios. The paper is organized into sections reviewing past efforts, discussing future research directions, and presenting concluding comments. The review classifies past DTA approaches into four broad methodological groups: mathematical programming, optimal control, variational inequality, and simulation-based.Dynamic Traffic Assignment (DTA) has evolved significantly since its pioneering work by Merchant and Nemhauser. This special issue aims to document the main existing DTA approaches for future reference. The paper provides an overview of the current understanding of DTA, reviews the existing literature, connects it to the approaches presented in the special issue, and hypothesizes about the future. DTA refers to a broad spectrum of problems, each with different decision variables, behavioral assumptions, and data requirements. The general DTA problem is characterized by ill-behaved system properties due to time-varying flows and randomness in system inputs. This complexity has led to a dichotomy of approaches, ranging from analytical to simulation-based methods. Despite the theoretical intractability, practical solutions have been developed that are effective and efficient for realistic scenarios. The paper is organized into sections reviewing past efforts, discussing future research directions, and presenting concluding comments. The review classifies past DTA approaches into four broad methodological groups: mathematical programming, optimal control, variational inequality, and simulation-based.