Coherence is an important property of laser beam, and laser beam with low spatial coherence is called partially coherent beam. Coherence structure is an unique parameter of partially coherent beams, and partially coherent beams with special coherence structure can be generated by manipulating their coherence properties. Partially coherent beams with special coherence structure not only exhibit many interesting propagation properties, but also can suppress the negative effects of atmospheric turbulence, such as degradation of intensity and coherence distribution, beam wander and scintillation, which have many application prospects in free-space optical communications, remote sensing, active laser radar systems, and so on. Recently, more and more attention is being paid to the propagation of partially coherent beams with special coherence structure in turbulent atmosphere. The research methods and development of partially coherent beams with special correlation structure are reviewed, and the propagation properties of partially coherent beams with Hermite series coherence structure in turbulent atmosphere are illustrated as examples.