  The title of the paper coincides with the title of a paragraph in the famous
book by U. Frisch (1995)on classical turbulence. In this paragraph the author
discussed the role of statistical dynamics of vortex filaments in the theory of
turbulence and put the above question. In other words, whether the main
properties of turbulence (cascade, scaling laws) are the sequence of the vortex
line dynamics or the latter have only marginal signature. Quantum fluids, where
the vortex filaments are the real objects, give an excellent opportunity to
explore the role of discrete vortices in turbulent phenomena. The aim of this
paper is to discuss which elements of vortex dynamics would lead to the main
ingredients of the theory of turbulence. We discuss how the nonlinear dynamics
of vortex filaments can result in an exchange of energy between different
scales, the formation of the Kolmogorov-type energy spectra and the decay of
turbulence.
