I’ll discuss joint work with Michael Landry and Yair Minsky that characterizes the surfaces in a compact 3-manifold M that are (almost) transverse to a fixed transitive pseudo-Anosov flow. Our main tool is a general correspondence between surfaces that are almost transverse to the flow and those that are “relatively carried” by any associated veering triangulation. The correspondence also allows us to investigate the uniqueness of almost transverse position, to extend Mosher's Transverse Surface Theorem to the case with boundary, and more generally to characterize when relative homology classes represent Birkhoff surfaces of the flow.