Abstract
The problems and prospects of statistical modeling of energy containing structure of developed turbulent flows are shown.It is shown that the method of RANS can not provide high quality of such models due to unconditional averaging of Navier-Stokes equations.Also, it is shown that high quality of mathematical models can be achieved using the method of autonomous statistical modeling of turbulence ASMTurb, distinctive feature of which is conditional averaging of Navier-Stokes equations over a turbulent and non-turbulent fluid of a turbulent flow.