This colloquium discusses the creation of artificial gauge potentials for neutral atoms, which can mimic the dynamics of charged particles in a magnetic field. The authors present the physical principles behind this phenomenon, relating the resulting Aharonov–Bohm phase to the Berry’s phase that arises when an atom follows an adiabatically dressed state. They explore the manifestations of artificial magnetism in cold quantum gases, particularly in terms of vortex nucleation. The discussion extends to the simulation of non-Abelian gauge potentials, highlighting their striking consequences such as effective spin-orbit coupling. The analysis covers both bulk gases and discrete systems, including optical lattices. The colloquium is organized into several sections, starting with a toy model of a two-level atom in a light beam, followed by detailed discussions on gauge potentials for multi-level systems, non-Abelian gauge potentials, and their implementation in optical lattices. The authors also address the validity of the adiabatic approximation and provide practical implementations using alkaline-earth atoms.This colloquium discusses the creation of artificial gauge potentials for neutral atoms, which can mimic the dynamics of charged particles in a magnetic field. The authors present the physical principles behind this phenomenon, relating the resulting Aharonov–Bohm phase to the Berry’s phase that arises when an atom follows an adiabatically dressed state. They explore the manifestations of artificial magnetism in cold quantum gases, particularly in terms of vortex nucleation. The discussion extends to the simulation of non-Abelian gauge potentials, highlighting their striking consequences such as effective spin-orbit coupling. The analysis covers both bulk gases and discrete systems, including optical lattices. The colloquium is organized into several sections, starting with a toy model of a two-level atom in a light beam, followed by detailed discussions on gauge potentials for multi-level systems, non-Abelian gauge potentials, and their implementation in optical lattices. The authors also address the validity of the adiabatic approximation and provide practical implementations using alkaline-earth atoms.