This Colloquium discusses the concept of artificial gauge potentials for neutral atoms, which mimic the behavior of charged particles in magnetic fields. The key idea is that neutral atoms can acquire a geometric phase when moving through a laser field, similar to the Aharonov-Bohm phase in electromagnetism. This geometric phase arises from the adiabatic following of dressed states, which are eigenstates of the atom-light interaction. The paper explores both Abelian and non-Abelian gauge potentials, with applications to cold quantum gases, including the generation of vortices and spin-orbit coupling. It also addresses the simulation of non-Abelian gauge fields in optical lattices and discusses the physical interpretation of these fields. The paper emphasizes the importance of geometric phases in quantum mechanics and their role in creating artificial magnetic fields for neutral atoms. It also discusses the practical implementation of these concepts using various laser configurations, such as those with orbital angular momentum or spatially shifted beams. The paper concludes with an outlook on future research directions and potential applications of artificial gauge potentials in quantum simulations.This Colloquium discusses the concept of artificial gauge potentials for neutral atoms, which mimic the behavior of charged particles in magnetic fields. The key idea is that neutral atoms can acquire a geometric phase when moving through a laser field, similar to the Aharonov-Bohm phase in electromagnetism. This geometric phase arises from the adiabatic following of dressed states, which are eigenstates of the atom-light interaction. The paper explores both Abelian and non-Abelian gauge potentials, with applications to cold quantum gases, including the generation of vortices and spin-orbit coupling. It also addresses the simulation of non-Abelian gauge fields in optical lattices and discusses the physical interpretation of these fields. The paper emphasizes the importance of geometric phases in quantum mechanics and their role in creating artificial magnetic fields for neutral atoms. It also discusses the practical implementation of these concepts using various laser configurations, such as those with orbital angular momentum or spatially shifted beams. The paper concludes with an outlook on future research directions and potential applications of artificial gauge potentials in quantum simulations.