Partially coherent beam is preferred in many applications, such as free-space optical communications, remote sensing, active laser radar systems, etc., due to its resistance to the deleterious effects of atmospheric turbulence. In this paper, after presenting a historical overview on propagation of optical beams in turbulent atmosphere, we describe the basic theory for treating the propagation of optical beams in turbulent atmosphere and we mainly introduce recent theoretical and experimental developments on propagation of partially coherent beam in turbulent atmosphere. Recent progress on the interaction of a partially coherent beam with a semirough target in turbulent atmosphere and the corresponding inverse problem are also reviewed.