This text places emphasis on the fact that the statistical laws in turbulence are not disconnected with the coherent structures distributing randomly in space and forming/decaying spontaneously in time, and that the anomalous scaling laws of a passive scalar in turbulence are captured from the first principle. Existence of such coherences in the stochastic processes of turbulence leads to the intermittency and also non-Gaussian statistics. Details of the geometrical structures are investigated how they are described in terms of vortices of shear layers.