Contents

Abstract. This article is an unorthodox survey of Finsler geometry presenting both results and open problems. It aims to show that re-cent progress in convex geometry, the calculus of variations, symplectic geometry, and integral geometry can be powerful tools in the study of Finsler manifolds; and that Finsler geometry can prove useful in solving some of the open problems in these fields. We do like intuitive geometric arguments and uncovering simple geometric reasons underlying seemingly recondite facts