  The aim of this (mostly expository) article is twofold. We first explore a
variety of length functions on the space of currents, and we survey recent work
regarding applications of length functions to counting problems. Secondly, we
use length functions to provide a proof of a folklore theorem which states that
pseudo-Anosov homeomorphisms of closed hyperbolic surfaces act on the space of
projective geodesic currents with uniform north-south dynamics.
