The Lefschetz-Hopf trace formula is a beautiful topological statement that relates the fixed points of a map to an alternating sum of traces on homology groups. The related Poincaré-Hopf index formula computes the Euler characteristic of a space in terms of the zeros of a vector field. In my talk, I want to present analogous statements in tropical geometry, in particular, for matroid fans. In doing so, we use two ingredients that have received much attention over the last years: tropical homology on the homology side and tropical intersection theory on the fixed point/vector field side. The two sides will be connected using a certain variant of the beta invariant.