元胞自动机（CA）是一类定义在格点上的离散时间动力系统，其演化由局部更新规则决定。尽管定义简单，CA 却能展现出统计物理中诸多核心的宏观现象：平衡态与非平衡态相变、输运行为与流体力学极限、动力学粗糙化、自组织临界性，以及复杂的时空关联。本综述聚焦于三个紧密关联的主题：（i）将 CA 视为构型空间上平移交换映射，从结构角度进行刻画，重点讨论规则复杂性、可逆性及守恒律（包括离散连续性方程）；（ii）将 CA 中的输运行为划分为弹道型、扩散型与反常型三类，并通过 Green–Kubo 公式、标度理论及普适性类，将微观流与宏观定律相联系；（iii）发展基于关联的方法——涵盖结构因子与响应公式、计算力学及数据驱动推断——以识别不同物态并实现粗粒化描述。

Cellular automata (CA) are discrete-time dynamical systems with local update rules on a lattice. Despite their elementary definition, CA support a wide spectrum of macroscopic phenomena central to statistical physics: equilibrium and nonequilibrium phase transitions, transport and hydrodynamic limits, kinetic roughening, self-organized criticality, and complex spatiotemporal correlations. This survey focuses on three tightly connected themes. \emph{(i)} We present a structural view of CA as shift-commuting maps on configuration spaces, emphasizing rule complexity, reversibility, and conservation laws (including discrete continuity equations). \emph{(ii)} We organize transport in CA into ballistic, diffusive, and anomalous regimes, and connect microscopic currents to macroscopic laws through Green--Kubo formulas, scaling theory, and universality classes. \emph{(iii)} We develop correlation-based methods -- from structure factors and response formulas to computational mechanics and data-driven inference -- that diagnose regimes and enable coarse-graining.