The study of pseudo-Anosov homeomorphisms of surfaces can be understood via train tracks carrying the stable and unstable laminations. After Hamenstadt, one has a splitting complex, which gives rise to a dual triangulation of the punctured mapping torus known as a veering triangulation. I'll discuss the combinatorial properties of these triangulations, and survey some of the literature on the topic. Applications include the conjugacy problem, describing short geodesics in moduli spaces, and relations with hyperbolic geometry.