Theoretically analytic methods and numerical simulation algorithms used to investigate the propagation of a partially coherent beam in turbulent atmosphere are briefly reviewed. Theoretical methods include extended Huygens-Fresnel principle, cross-spectral density function, coherent-mode decomposition, effective beam parameters and ABCD ray matrix. The simulation algorithms contain random phase screen, coherentmode recomposition and random optical pulse method. Several typical types of partially coherent beam and beam spreading of a partially coherent beam in free space are introduced. Main results as to beam spreadzing, optical intensity fluctuation and angle-of-arrival fluctuation in turbulent atmosphere are summarized.Problems that should be further studied are presented.