Light propagation through non-Kolmogorov atmospheric turbulence and its effects on optical engineering are focus of applied optics research. Discussion and comparison are carried out for the optical properties of real atmospheric turbulence and theoretical models of non-Kolmogorov turbulence. Recent research progress in last five years is summarized and related problems are analyzed on general propagation effects, effects in anisotropic turbulence, propagation of special beams, partially coherent beams and beam arrays, and these effects on optical engineering. Suggestions are proposed for next step on the monitoring technology of atmospheric turbulence, numerical simulation of light propagation through non-Kolmogorov turbulence and experimental study in real atmosphere.