The famous 1939 Myers–Steenrod theorem states that a distance preserving map between (smooth) Riemannian manifolds is actually a smooth isometry. In this talk I will give a similar statement for Finsler manifolds under minimal regularity (i.e. we do not assume the metric to be smooth). I shall explain the concepts from Finsler geometry that are needed as well as some history (Riemannian and Finslerian) of the subject. I will give a sketch of the proof and discuss some related results.