This article provides a comprehensive review of the statistical physics of vehicular traffic, focusing on both microscopic and macroscopic models. The authors, Debashish Chowdhury, Ludger Santen, and Andreas Schadschneider, from the Institute for Theoretical Physics at the University of Cologne, discuss the fundamental aspects of traffic phenomena from a statistical physics perspective. They explore various theoretical approaches, including fluid-dynamical theories, kinetic theories, and car-following theories, as well as particle-hopping models formulated using cellular automata (CA). The review highlights the rich variety of physical phenomena observed in vehicular traffic, such as transitions between dynamical phases, criticality, self-organized criticality, metastability, hysteresis, and phase segregation. The authors explain the guiding principles behind different theoretical approaches and present detailed discussions on results from particle-hopping models, particularly those formulated using CA. Key topics covered include: - **Fundamental and Practical Questions**: The aim of basic research in traffic science is to discover fundamental laws governing traffic systems, while traffic engineering focuses on planning, design, and implementation of transportation networks. - **Empirical Facts and Phenomenological Explanations**: The article discusses empirical data on acceleration noise, the formation and characterization of traffic jams, and the flux-density relation. - **Fluid-Dynamical Theories**: These theories treat traffic as a compressible fluid, with the Lighthill-Whitham theory and the Greenshields model being key components. The Lighthill-Whitham theory assumes that the flux is a function of density, leading to the concept of kinematic waves. - **Kinetic Theories**: These theories modify the kinetic theory of gases to describe the motion of individual vehicles. - **Car-Following Theories**: These theories are based on classical Newtonian dynamics and describe the motion of vehicles based on their neighbors' positions and velocities. - **Particle-Hopping Models**: These models describe traffic dynamics using stochastic dynamics of individual vehicles, with the Nagel-Schreckenberg (NaSch) model being a minimal example of highway traffic. The article also addresses practical applications of these models, such as on-ramp and off-ramp design, lane improvements, and signaling strategies. It concludes with a discussion on the similarities between various particle-hopping models and other systems far from equilibrium, emphasizing the universal nature of certain physical phenomena.This article provides a comprehensive review of the statistical physics of vehicular traffic, focusing on both microscopic and macroscopic models. The authors, Debashish Chowdhury, Ludger Santen, and Andreas Schadschneider, from the Institute for Theoretical Physics at the University of Cologne, discuss the fundamental aspects of traffic phenomena from a statistical physics perspective. They explore various theoretical approaches, including fluid-dynamical theories, kinetic theories, and car-following theories, as well as particle-hopping models formulated using cellular automata (CA). The review highlights the rich variety of physical phenomena observed in vehicular traffic, such as transitions between dynamical phases, criticality, self-organized criticality, metastability, hysteresis, and phase segregation. The authors explain the guiding principles behind different theoretical approaches and present detailed discussions on results from particle-hopping models, particularly those formulated using CA. Key topics covered include: - **Fundamental and Practical Questions**: The aim of basic research in traffic science is to discover fundamental laws governing traffic systems, while traffic engineering focuses on planning, design, and implementation of transportation networks. - **Empirical Facts and Phenomenological Explanations**: The article discusses empirical data on acceleration noise, the formation and characterization of traffic jams, and the flux-density relation. - **Fluid-Dynamical Theories**: These theories treat traffic as a compressible fluid, with the Lighthill-Whitham theory and the Greenshields model being key components. The Lighthill-Whitham theory assumes that the flux is a function of density, leading to the concept of kinematic waves. - **Kinetic Theories**: These theories modify the kinetic theory of gases to describe the motion of individual vehicles. - **Car-Following Theories**: These theories are based on classical Newtonian dynamics and describe the motion of vehicles based on their neighbors' positions and velocities. - **Particle-Hopping Models**: These models describe traffic dynamics using stochastic dynamics of individual vehicles, with the Nagel-Schreckenberg (NaSch) model being a minimal example of highway traffic. The article also addresses practical applications of these models, such as on-ramp and off-ramp design, lane improvements, and signaling strategies. It concludes with a discussion on the similarities between various particle-hopping models and other systems far from equilibrium, emphasizing the universal nature of certain physical phenomena.