In this talk, we will first introduce the notion of Finsler metric and will describe several applications. Then we will introduce anisotropic tensors, explaining why they are a key ingredient when dealing with Finsler metrics. Finally we will show how to define derivations of anisotropic tensors using an anisotropic connection. In particular, this will allow us to interpret the Chern connection as the Levi-Civita connection and to define the Lie derivative of anisotropic tensors.