In this talk, I will first explain the basic idea of Witten's loop space construction of elliptic genus. Then I will briefly discuss the proof of Witten's rigidity theorem as well as its family generalizations. At last, I will talk about my joint work with Bo LIU, the Witten rigidity theorem on Z/k manifolds (arxiv 1104.3972) and String^c manifolds (arxiv 1206.5955).