The logarithmic law in mean velocity has been the most important landmark in research of wall turbulence roughly for a century. The growing evidence indicates that such a log law appears even in higher statistical moments, such as turbulence intensity. In this talk, we will review the early development of the ideas on the log law by the 20th century’s giants in turbulence research with emphasis on appropriate reinterpretations in the modern setting. In particular, we will propose that the emergence of the logarithms in wall turbulence is conceptually linked with a hierarchical organisation of the invariant solutions of the Navier-Stokes equations (e.g. relative equilibria and periodic orbits), that have played the central role in the current understanding of transition to turbulence.