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A global section to a flow on a 3-manifold is a closed cooriented embedded surface that is positively transverse to the flow lines. A Birkhoff section is a generalization where one allows the surface to admit boundary components tangent to the flow. Using Birkhoff sections, one can convert between dynamical information of 3-dimensional flows and 2-dimensional maps. A classical result of Fried states that every transitive Anosov flow admits a Birkhoff section. The natural next question is how simple of a Birkhoff section we can find. In this talk, we discuss some recent progress on this question.