  Volterra functions were introduced at the beginning of the twentieth century
as solutions of some integral equations of convolution type with logarithmic
kernel. Since then, few authors have studied this family of functions and faced
with the problem of providing a clear understanding of their asymptotic
behaviour for small and large arguments. This paper reviews some of the most
important results on Volterra functions and in particular collects, into a
quite general framework, several results on their asymptotic expansions, these
results turn out to be useful not only for the full understanding of the
behaviour of the Volterra functions but also for their numerical computation.
The connections with integrals of Ramanujan type, which have several important
applications, are also discussed.
