This review focuses on the creation and application of gauge fields in ultracold atomic systems. Gauge fields are fundamental to modern physics, governing interactions at various scales from high-energy particle physics to condensed matter systems. In ultracold atomic systems, gauge fields are engineered by coupling atoms to laser fields, creating effective gauge potentials that mimic the behavior of magnetic and electric fields. These synthetic gauge potentials can be Abelian or non-Abelian and are used to simulate quantum systems with exotic properties, such as topological states and interacting gauge theories. The review covers techniques for creating these gauge potentials, including rotating and shaking systems, geometric gauge potentials, and driven-induced topological phases. It also discusses the implications of these synthetic fields in quantum simulation, topological matter, and the simulation of interacting gauge theories. The review concludes by highlighting the potential applications of these techniques in advancing our understanding of complex physical systems.This review focuses on the creation and application of gauge fields in ultracold atomic systems. Gauge fields are fundamental to modern physics, governing interactions at various scales from high-energy particle physics to condensed matter systems. In ultracold atomic systems, gauge fields are engineered by coupling atoms to laser fields, creating effective gauge potentials that mimic the behavior of magnetic and electric fields. These synthetic gauge potentials can be Abelian or non-Abelian and are used to simulate quantum systems with exotic properties, such as topological states and interacting gauge theories. The review covers techniques for creating these gauge potentials, including rotating and shaking systems, geometric gauge potentials, and driven-induced topological phases. It also discusses the implications of these synthetic fields in quantum simulation, topological matter, and the simulation of interacting gauge theories. The review concludes by highlighting the potential applications of these techniques in advancing our understanding of complex physical systems.