The notion of positive isotropic curvature was introduced in 1988 by Micallef and Moore. Since then this curvature condition has been extensively investigated. In this talk I’ll mainly focus on the topological implications of this curvature condition. First I’ll briefly survey some of the previous works by various authors on Riemannian manifolds with positive isotropic curvature, including those by Brendle, Chen-Tang-Zhu, Chen-Zhu, Fraser, Hamilton, et al. Then I’ll introduce my recent work on the topological classification of compact manifolds of dimension

n ≥ 12 with positive isotropic curvature, which uses Ricci flow with surgery on orbifolds with the help of techniques from differential topology.