Abstract: With laser beam propagating over a long distance through even weak atmospheric turbulence,significant turbulence effect might happen so that a continuous phase function does not exist in general owing to the presence of branch points in phase.Branch points could induce degradation of the performance of a standard adaptive optics system when it is used to compensate atmospheric turbulence.The generation and development,the optical properties and topological characteristics of branch points in the atmosphere were introduced.The study of phase discontinuity of laser propagation through atmosphere was reviewed so as to provide a reference for further study of laser propagation through atmosphere and adaptive optics system.