  We survey some of our recent results on length series identities for
hyperbolic (cone) surfaces, possibly with cusps and/or boundary geodesics;
classical Schottky groups; representations/characters of the one-holed torus
group to $SL(2, \mathbf C)$; and hyperbolic 3 manifolds obtained by hyperbolic
Dehn surgery on punctured torus bundles over the circle. These can be regarded
as generalizations and variations of McShane's identity for cusped hyperbolic
surfaces, which has found some striking applications in the recent work of
Mirzakhani. We discuss some of the methods and techniques used to obtain these
identities.
