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Some links between Lorentz and Finsler geometries have been developed in thelast years, with applications even to the Riemannian case. Our purpose is togive a brief description of them, which may serve as an introduction to recentreferences. As a motivating example, we start with Zermelo navigation problem,where its known Finslerian description permits a Lorentzian picture whichallows for a full geometric understanding of the original problem. Then, wedevelop some issues including: (a) the accurate description of the Lorentziancausality using Finsler elements, (b) the non-singular description of someFinsler elements (such as Kropina metrics or complete extensions of Randersones with constant flag curvature), (c) the natural relation between theLorentzian causal boundary and the Gromov and Busemann ones in the Finslersetting, and (d) practical applications to the propagation of waves andfirefronts.

An account on links between Finsler and Lorentz Geometries for Riemannian Geometers