Rydberg atom arrays have emerged as a novel platform for studying quantum many-body physics and universal quantum computation. The Rydberg blockade effect, which arises from the strong dipole interactions between Rydberg states, plays a crucial role in establishing many-body correlations in these systems. This review highlights the lattice gauge theory as an efficient description of the Rydberg blockade effect and discusses recent developments in this system, including the realization of exotic ground states such as spin liquids, the discovery of quantum many-body scar states that violate quantum thermalization, and the observation of confinement-deconfinement transitions through quantum dynamics. The review begins by introducing the Rydberg atom arrays and the Rydberg blockade effect, emphasizing the strong dipole interactions and the metastable states of Rydberg atoms. It then delves into the theoretical framework of the PXP model, which captures the essential features of the Rydberg blockade effect. The PXP model is shown to be a lattice gauge theory, similar to the one-dimensional lattice Schwinger model, and it naturally explains various phenomena in the system. The review further explores the emergence of gauge symmetry in the context of the Rydberg atom arrays, comparing it with the emergence of gauge symmetry in strongly correlated systems like the Hubbard model. It discusses the ground state properties of different array geometries, including the spin liquid state in the Kagome lattice, and the variational wave functions that can describe these states. The review also examines the quantum many-body scar states, which are non-thermal excited states that violate the eigenstate thermalization hypothesis. These scar states are shown to be connected to the critical states at the quantum phase transition, and their properties are analyzed in detail. Finally, the review discusses the confinement-deconfinement dynamics across the Ising transition, which can be probed through quench dynamics. The potential of Rydberg atom arrays for fault-tolerant universal quantum computation is highlighted, along with the connection between local gauge symmetry and quantum error correction codes. Overall, the review provides a comprehensive overview of the recent advancements in the study of Rydberg atom arrays, emphasizing the role of the gauge theory description in capturing the rich quantum many-body physics and its implications for future quantum simulations and quantum computation.Rydberg atom arrays have emerged as a novel platform for studying quantum many-body physics and universal quantum computation. The Rydberg blockade effect, which arises from the strong dipole interactions between Rydberg states, plays a crucial role in establishing many-body correlations in these systems. This review highlights the lattice gauge theory as an efficient description of the Rydberg blockade effect and discusses recent developments in this system, including the realization of exotic ground states such as spin liquids, the discovery of quantum many-body scar states that violate quantum thermalization, and the observation of confinement-deconfinement transitions through quantum dynamics. The review begins by introducing the Rydberg atom arrays and the Rydberg blockade effect, emphasizing the strong dipole interactions and the metastable states of Rydberg atoms. It then delves into the theoretical framework of the PXP model, which captures the essential features of the Rydberg blockade effect. The PXP model is shown to be a lattice gauge theory, similar to the one-dimensional lattice Schwinger model, and it naturally explains various phenomena in the system. The review further explores the emergence of gauge symmetry in the context of the Rydberg atom arrays, comparing it with the emergence of gauge symmetry in strongly correlated systems like the Hubbard model. It discusses the ground state properties of different array geometries, including the spin liquid state in the Kagome lattice, and the variational wave functions that can describe these states. The review also examines the quantum many-body scar states, which are non-thermal excited states that violate the eigenstate thermalization hypothesis. These scar states are shown to be connected to the critical states at the quantum phase transition, and their properties are analyzed in detail. Finally, the review discusses the confinement-deconfinement dynamics across the Ising transition, which can be probed through quench dynamics. The potential of Rydberg atom arrays for fault-tolerant universal quantum computation is highlighted, along with the connection between local gauge symmetry and quantum error correction codes. Overall, the review provides a comprehensive overview of the recent advancements in the study of Rydberg atom arrays, emphasizing the role of the gauge theory description in capturing the rich quantum many-body physics and its implications for future quantum simulations and quantum computation.