For experimenters, coherent structures (CSs) in a turbulent flow appear as macroscopic subdomains of coherently moving volumes amid apparent chaos. Despite the undoubted importance of CSs, the process of their appearance remains unclear. In fact, this problem is related to the more general problem of the emergence of order in chaos and out of chaos in several natural phenomena. Turbulence theory has evolved in the opposite direction during many years. Since the fundamental paper of Kolmogorov, who proposed the concept of the “direct cascade” of energy transfer to all decreasing typical vortex dimensions, the emphasis was on statistical concepts of “chaotization” of turbulent flows. The initial 3-D Navier–Stokes equations in fact remained in the shadows.