In this talk, we will introduce the notion of an end-periodic homeomorphism of an infinite-type surface. We will explore how the geometry of the associated mapping torus is related to certain topological and dynamical features of the end-periodic gluing map. In particular, we will see how the hyperbolic volume of the 3-manifold can be bounded both above and below in terms of a certain dynamical feature of the homeomorphism. This talk represents joint work with Autumn Kent, Heejoung Kim, Christopher Leininger, and Marissa Loving (in various configurations)