The curve, pants, and arc complexes of a surface S are simplicial complexes which encode information about hyperbolic 3-manifolds fibering over the circle with fiber S. Unfortunately, it is not very clear how the combinatorics of any of these complexes depends on the choice of surface, S, and this makes it difficult to extract concrete information about hyperbolic manifolds. In this talk we will summarize some recent progress towards understanding this dependence, and present an application: an "effective" version of a theorem of Brock which relates the volume of a fibered hyperbolic 3-manifold with fiber S, to the action of its monodromy on the pants complex. Some of this is joint work with Samuel Taylor and Richard Webb.