Rydberg atom arrays have emerged as a promising platform for studying quantum many-body physics and quantum computation. The Rydberg blockade effect, which prevents two Rydberg atoms from being close to each other, plays a key role in establishing many-body correlations. This review highlights that the lattice gauge theory provides an efficient description of the Rydberg blockade effect and summarizes 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 gauge theory description offers a universal theoretical framework to capture these phenomena. Gauge symmetry is a fundamental symmetry in nature and plays an essential role in the standard model of particle physics. It also appears as an emergent symmetry in the low-energy effective theory of strongly correlated condensed matter systems. The Rydberg blockade effect, which arises from the strong dipolar interaction between Rydberg atoms, leads to the emergence of a gauge theory in Rydberg atom arrays. This gauge theory naturally captures the Rydberg blockade-induced correlation effects both in and out of equilibrium. The Rydberg blockade effect can be described by the PXP model, which is a lattice gauge theory. The PXP model has been shown to exhibit a variety of interesting phenomena, including quantum spin liquid states and quantum many-body scar states. The gauge theory description of the PXP model has also been extended to two-dimensional Rydberg arrays, including the Kagome lattice, where spin liquid states have been observed. The Rydberg atom arrays also exhibit rich quantum dynamics, including the confinement-deconfinement transition across the Ising transition. This transition can be probed by studying quench dynamics and has been observed in optical lattice-simulated PXP models. The Rydberg atom arrays also have great potential for fault-tolerant universal quantum computation, as both many-body correlation and two-qubit CNOT gates originate from the same Rydberg blockade effect. Understanding emergent gauge symmetry from correlation effects can eventually help with quantum error correction in this platform.Rydberg atom arrays have emerged as a promising platform for studying quantum many-body physics and quantum computation. The Rydberg blockade effect, which prevents two Rydberg atoms from being close to each other, plays a key role in establishing many-body correlations. This review highlights that the lattice gauge theory provides an efficient description of the Rydberg blockade effect and summarizes 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 gauge theory description offers a universal theoretical framework to capture these phenomena. Gauge symmetry is a fundamental symmetry in nature and plays an essential role in the standard model of particle physics. It also appears as an emergent symmetry in the low-energy effective theory of strongly correlated condensed matter systems. The Rydberg blockade effect, which arises from the strong dipolar interaction between Rydberg atoms, leads to the emergence of a gauge theory in Rydberg atom arrays. This gauge theory naturally captures the Rydberg blockade-induced correlation effects both in and out of equilibrium. The Rydberg blockade effect can be described by the PXP model, which is a lattice gauge theory. The PXP model has been shown to exhibit a variety of interesting phenomena, including quantum spin liquid states and quantum many-body scar states. The gauge theory description of the PXP model has also been extended to two-dimensional Rydberg arrays, including the Kagome lattice, where spin liquid states have been observed. The Rydberg atom arrays also exhibit rich quantum dynamics, including the confinement-deconfinement transition across the Ising transition. This transition can be probed by studying quench dynamics and has been observed in optical lattice-simulated PXP models. The Rydberg atom arrays also have great potential for fault-tolerant universal quantum computation, as both many-body correlation and two-qubit CNOT gates originate from the same Rydberg blockade effect. Understanding emergent gauge symmetry from correlation effects can eventually help with quantum error correction in this platform.