Theoretical models and results of experimental campaigns relating to non-classic regimes occurring in atmospheric optical turbulence are overviewed. Non-classic turbulence may manifest itself through such phenomena as a varying power law of the refractive-index power spectrum, anisotropy, the presence of constant-temperature gradients and coherent structures. A brief historical introduction to the theories of optical turbulence, both classic and non-classic, is first presented. The effects of non-classic atmospheric turbulence on propagating light beams are then discussed, followed by the summary of results on measuring the non-classic turbulence, on its computer and in-lab simulations and its controlled synthesis. The general theory based on the extended Huygens-Fresnel method, capable of quantifying various effects of non-classic turbulence on propagating optical fields, including the increased light diffraction, beam profile deformations, etc., is then outlined. The review concludes by a summary of optical engineering applications that can be influenced by atmospheric non-classic turbulence, e.g., remote sensing, imaging and wireless optical communication systems. The review makes an accent on the results developed by the authors for the recent AFOSR MURI project on deep turbulence.
