In 1972, J. Norbury discovered a new family of steady vortex rings by perturbing the well-known Hill's spherical vortex, now known as Norbury's vortex rings. This talk will present recent stability results for Norbury's vortex rings. The proof relies on the classical variational principle, combined with Amick-Fraenkel's local uniqueness result and some compactness theorems from Kyudong Choi's  breakthrough work on the stability of Hill's spherical vortex.   Some related open problems will also be discussed. This talk is based on joint work with Daomin Cao, Weicheng Zhan and Changjun Zou.