  In this second part of our overview of the different metric curvatures and
their various applications, we concentrate on the Ricci curvature and flow for
polyhedral surfaces and higher dimensional manifolds, and we largely review our
previous studies on the subject, based upon Wald's curvature. In addition to
our previous metric approaches to the discretization of Ricci curvature, we
consider yet another one, based on the Haantjes curvature, interpreted as a
geodesic curvature. We also try to understand the mathematical reasons behind
the recent proliferation of discretizations of Ricci curvature. Furthermore, we
propose another approach to the metrization of Ricci curvature, based on
Forman's discretization, and in particular we propose on that uses our graph
version of Forman's Ricci curvature.
