The conformal dimension of a compact metric space is defined as the infimum of the Hausdorff dimension in its quasi-symmetric equivalence class. It has been proven that many properties of Gromov hyperbolic groups are explained by conformal dimensions of their boundaries at infinity. In this talk, we discuss conformal dimensions of Julia sets, that are repellers of dynamical systems defined by iteration of rational maps on the Riemann sphere. Especially, we discuss the family of post-critically finite hyperbolic rational maps whose Julia sets have conformal dimension 1.