Abstract: A pseudo-Anosov flow on a 3-manifold is a natural generalization of the suspension flow of a pseudo-Anosov surface diffeomorphism. If a properly embedded surface is transverse to such a flow, then a result of Mosher says it is Thurston norm minimizing in its homology class. Given a pseudo-Anosov flow, one might ask "to which surfaces is the flow transverse?" Alternatively, given a norm minimizing surface, one might ask "to which pseudo-Anosov flows is the surface transverse?" I will give some of the history of these questions and state a few new results, motivated by larger questions about the Thurston norm. Some of this is joint work with Chi Cheuk Tsang and some is joint with Yair Minsky and Sam Taylor.