In this talk, I will describe a couple of cases in which Finsler geometry leads to connections with special holonomy. In particular, I will describe how a Finsler metric with constant positive flag curvature induces a canonical Kahler metric on its space of geodesics and how certain such Finsler metrics determine (and are determined by) spaces carrying a torsion-free connection whose holonomy is 'exotic' in the sense that it is not on the lists of the currently accepted groups that can be holonomy of torsion-free connections.