We provide a review of the theoretical research progress on the influence of atmospheric turbulence and thermal blooming on the characteristics and beam quality of laser array beams propagating in the atmosphere. The analytical and numerical simulation methods to study the propagation of laser array beams in the atmosphere are introduced. The influence of the atmospheric turbulence on the intensity, angular spread, directionality, curvature radius and turbulence distance of laser array beams is reviewed, and the influence of the atmospheric thermal blooming on the intensity, propagation efficiency, beam centroid, time scale of thermal blooming and focal shift of laser array beams is also reviewed. It is shown that the influence of atmospheric turbulence and thermal blooming on the beam quality of laser array beams is closely related with the beam combination methods, beam parameters and atmospheric parameters.