Dynamic Traffic Assignment (DTA) has evolved significantly since the pioneering work of Merchant and Nemhauser. This paper summarizes current understanding of DTA, reviews existing literature, connects it to approaches in this special issue, and hypothesizes about the future. DTA addresses time-varying traffic flows, departing from static assignment assumptions. It encompasses a broad range of problems with varying decision variables, behavioral assumptions, and data requirements. Current DTA models lack a universal solution for general networks and are characterized by ill-behaved system properties due to the need to represent traffic realism and human behavior. Time-dependency and randomness in system inputs exacerbate this complexity. Theoretical guarantees of properties like existence, uniqueness, and stability are limited due to the need to compromise on traffic theoretical phenomena and driver behavior assumptions. This complexity has led to a dichotomy of approaches, ranging from analytical to simulation-based. Practical consequences of theoretical intractability have driven DTA researchers to focus on deployable solution procedures that seek near-optimal solutions. These procedures prioritize effectiveness, robustness, and deployment efficiency. The notion of commensurability among different approaches allows trade-offs in features to address varying DTA problems. Despite mathematical intractability, DTA has practical utility in real-world applications, as evidenced by effective solutions for realistic scenarios with mild violations. Different approaches address different functional needs with varying degrees of robustness, avoiding sweeping generalizations based on pathological scenarios. A deployable DTA approach should adequately represent traffic realism in the context of the problem objective. This paper reviews past DTA efforts, classifying approaches into four groups: mathematical programming, optimal control, variational inequality, and simulation-based. It discusses future research directions and concludes with comments on DTA's development.Dynamic Traffic Assignment (DTA) has evolved significantly since the pioneering work of Merchant and Nemhauser. This paper summarizes current understanding of DTA, reviews existing literature, connects it to approaches in this special issue, and hypothesizes about the future. DTA addresses time-varying traffic flows, departing from static assignment assumptions. It encompasses a broad range of problems with varying decision variables, behavioral assumptions, and data requirements. Current DTA models lack a universal solution for general networks and are characterized by ill-behaved system properties due to the need to represent traffic realism and human behavior. Time-dependency and randomness in system inputs exacerbate this complexity. Theoretical guarantees of properties like existence, uniqueness, and stability are limited due to the need to compromise on traffic theoretical phenomena and driver behavior assumptions. This complexity has led to a dichotomy of approaches, ranging from analytical to simulation-based. Practical consequences of theoretical intractability have driven DTA researchers to focus on deployable solution procedures that seek near-optimal solutions. These procedures prioritize effectiveness, robustness, and deployment efficiency. The notion of commensurability among different approaches allows trade-offs in features to address varying DTA problems. Despite mathematical intractability, DTA has practical utility in real-world applications, as evidenced by effective solutions for realistic scenarios with mild violations. Different approaches address different functional needs with varying degrees of robustness, avoiding sweeping generalizations based on pathological scenarios. A deployable DTA approach should adequately represent traffic realism in the context of the problem objective. This paper reviews past DTA efforts, classifying approaches into four groups: mathematical programming, optimal control, variational inequality, and simulation-based. It discusses future research directions and concludes with comments on DTA's development.