  This article is a report of Projet bibliographique of M1 at \'Ecole Normale
Sup\'erieure. In this article we reviewed the historical developments in
artificial gauge fields and spin-orbit couplings in cold atom systems. We
resorted to origins of literatures to trace the ideas of the developments. For
pedagogical purposes, we tried to work out examples carefully and clearly, to
verified the validity of various approximations and arguments in detail, and to
give clear physical and mathematical pictures of the problems that we
discussed. The first part of this article introduced the fundamental concepts
of Berry phase and Jaynes-Cummings model. The second part reviewed two schemes
to generate artificial gauge fields with N-pod scheme in cold atom systems. The
first one is based on dressed-atom picture which provide a method to generate
non-Abelian gauge fields with dark states. The second one is about rotating
scheme which is achieved earlier historically. Non-Abelian gauge field
inevitably leads to spin-orbit coupling. We reviewed some developments in
achieve spin-orbital coupling theoretically and experimentally. The fourth part
was devoted to recently developed idea of optical flux lattice that provides a
possibility to reach the strongly correlated regime in cold atom systems. We
developed a geometrical interpretation based on Cooper's theory. Some useful
formulae and their proofs were listed in the Appendix.
