In this talk, I will consider isomorphisms of Bergman fans of matroids. Motivated by algebraic geometry, such isomorphisms can be considered as matroid analogs of birational maps. If the matroids in question are not totally disconnected, I will explain that an isomorphism respecting their fine fan structures must be induced by a matroid isomorphism. However, if we switch to the coarse fan structure, this is no longer the case. I will introduce Cremona automorphisms of the coarse structure of certain Bergman fans. These produce a class of Bergman fan isomorphisms which are not induced by matroid automorphisms. I will then explain that the automorphism group of the coarse fan structure is generated by matroid automorphisms and Cremona maps in the case of rank 3 matroids which are not parallel connections and for modularly complemented matroids. This is based on joint work with Annette Werner.