Abstract: Flag curvature is the most important quantity in Finsler geometry, because it generalizes the notion of sectional curvature in Riemannian geometry. In this talk I will give a brief introduction to Finsler geometry and discuss some interesting curvature phenomena. In particular, I will prove that when flag curvature reduces to sectional curvature, then either the Finsler metric is Riemannian, or the flag curvature is isotropic (constant if the dimension is greater than two).