In this talk, I will discuss joint work with Samuel J. Taylor, where we consider embedded non-fiber surfaces in a closed hyperbolic 3-manifold transverse to a pseudo-Anosov flow. Utilizing foundational work on Kleinian surface groups, we connect geometric features of the surface and the 3-manifold, such as the volume and short geodesics, to the dynamics of the flow via the curve graph. I'll start by introducing pseudo-Anosov flows and discuss a dichotomy of transverse surfaces. Then I will explain how the curve graph is related to geometry, and how it is used in our work.