Refraction, turbulent scattering, and other atmospheric propagation effects complicate the performance of outdoor microphone arrays used to infer source bearings. In principle, with good knowledge of the atmospheric profiles, one can compensate for the refraction effects. However, the random angle‐of‐arrival variations induced by atmospheric turbulence limit array performance even when the signal‐to‐noise ratio is high. The turbulent scattering effect can be viewed as a coherence loss between elements of the beamforming array. Most research to date on acoustic signal coherence in the atmosphere has dealt with line‐of‐sight (LOS) propagation paths. A number of complications characteristic of real turbulence have been introduced; these include statistical inhomogeneity, anisotropy, and intermittency of the turbulent eddies. The LOS theory has also been extended to include sensor displacements longitudinal to the propagating wavefronts as well as transverse displacements. Formulations for the Cramer–Rao lower bound (CRLB) on the angle‐of‐arrival accuracy have been developed from the LOS theory. Based on limited experimental data and modeling, actual performance appears to be substantially worse than the CRLB. Recently, numerical methods have been introduced for solving second‐moment parabolic equations, which offer the possibility of incorporating non‐LOS effects into coherence calculations.