We analyze some recent publications addressing propagation of the partially coherent polarized beams and beam arrays in the turbulent atmosphere. We show that the published results are limited to the scalar propagation model, and are not particular to the beam polarization. Therefore these results are equally relevant for the scalar beam pairs and arrays discriminated by some parameters such as small frequency shift, time delay or geometry, but not necessary the polarization. We use the virtual incoherent source model to derive the general form of the mutual coherence function of the two Schell-type beams. We discuss some physical stochastic models that result in the creation of the Schell-type beams and beam arrays. New classes of the uniformly, nonuniformly and nonlocally coherent beam pairs emerge naturally from this analysis. Rigorous, Markov approximation-based, propagation model provides relatively simple analytic results for the second-order moments of the optical field of the partially-coherent individual beams and beam pairs. We examine the changes of the beam mutual coherence in the process of the free-space propagation and propagation through the turbulent atmosphere.© (2010) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.