  We start with a short survey of the basic properties of the Mittag-Leffler
functions. Then we focus on the key role of these functions to explain the
after-effects and relaxation phenomena occurring in dielectrics and in
viscoelastic bodies. For this purpose we recall the main aspects that were
formerly discussed by two pioneers in the years 1930's-1940's whom we have
identified with Harold T. Davis and Bernhard Gross.
