  When a neutral atom moves in a properly designed laser field, its
center-of-mass motion may mimic the dynamics of a charged particle in a
magnetic field, with the emergence of a Lorentz-like force. In this Colloquium
we present the physical principles at the basis of this artificial (synthetic)
magnetism and relate the corresponding Aharonov-Bohm phase to the Berry's phase
that emerges when the atom follows adiabatically one of its dressed states. We
also discuss some manifestations of artificial magnetism for a cold quantum
gas, in particular in terms of vortex nucleation. We then generalise our
analysis to the simulation of non-Abelian gauge potentials and present some
striking consequences, such as the emergence of an effective spin-orbit
coupling. We address both the case of bulk gases and discrete systems, where
atoms are trapped in an optical lattice.
