Following work of Schlenker, and inspired by Kojima and Macshane, we
recount new developments illustrating new connections between
Weil-Petersson geometry and 3-dimensional hyperbolic volume. These
connections give the first explicit lower bounds on the length of the
systole of moduli spaces of Riemann surfaces with the Weil-Petersson
metric in terms of volumes of hyperbolic mapping tori, and on the
diameters of moduli spaces of Riemann surfaces with the Weil-Petersson
metric. The results also give explicit upper and lower bounds on
Weil-Petersson distances between rational points in the boundary of
moduli space in terms of hyperbolic volume and the length of their
continued fraction expansions. This is joint work with Ken Bromberg.