  The paper {\it On the multifractal nature of fully developed turbulence and
chaotic systems}, by R. Benzi {\it et al.} published in this journal in 1984
(vol {\bf 17}, page 3521) has been a starting point of many investigations on
the different faces of selfsimilarity and intermittency in turbulent phenomena.
  Since then, the multifractal model has become a useful tool for the study of
small scale turbulence, in particular for detailed predictions of different
Eulerian and Lagrangian statistical properties. In the occasion of the 50-th
birthday of our unforgettable friend and colleague Giovanni Paladin
(1958-1996), we review here the basic concepts and some applications of the
multifractal model for turbulence.
