We will discuss various length series identities on hyperbolic surfaces and their applications
due to Basmajian, McShane, Mirzakhani, Bridgeman and various other authors. In particular,
we will present a unified approach for obtaining these identities and we will also discuss how this
can be used to derive a new identity for closed hyperbolic surfaces involving the dilogarithm of the lengths of simple closed geodesics, in recent joint work with Feng Luo.