Turbulence is ubiquitous in science, technology and daily life and yet, despite years of research, our understanding of its nature is still far from complete. The talk presents a review of studies of the fundamental nature of turbulence, in the light of high resolution direct numerical simulations of turbulence. An emphasis is placed upon the examination of the idea of celebrated Kolmogorov’s theory on the existence of the universality in the statistics at small scales in fully developed turbulence. A discussion is also given on an application of the idea of linear response theory developed in the statistical mechanics for non-equilibrium systems.