  Scale functions play a central role in the fluctuation theory of spectrally
negative L\'evy processes and often appear in the context of martingale
relations. These relations are often complicated to establish requiring
excursion theory in favour of It\^o calculus. The reason for the latter is that
standard It\^o calculus is only applicable to functions with a sufficient
degree of smoothness and knowledge of the precise degree of smoothness of scale
functions is seemingly incomplete. The aim of this article is to offer new
results concerning properties of scale functions in relation to the smoothness
of the underlying L\'evy measure. We place particular emphasis on spectrally
negative L\'evy processes with a Gaussian component and processes of bounded
variation.
  An additional motivation is the very intimate relation of scale functions to
renewal functions of subordinators. The results obtained for scale functions
have direct implications offering new results concerning the smoothness of such
renewal functions for which there seems to be very little existing literature
on this topic.
