Abstract: Gamma conjectures I, II and the underlying Conjecture O for Fano manifolds were proposed by Galkin, Golyshev and Iritani. In this talk, we will briefly review these conjectures, with an emphasis on counter-examples of Conjecture O and interesting questions arising from the counter-examples. This talk is based on joint work with S. Galkin, J. Hu, H. Iritani, H. Ke and Z. Su.