As generalizations of quantum groups, the i-quantum groups have recently drawn considerable attention because of its application in Kazhdan-Lusztig theory due to Bao and Wang. In this talk, we will introduce some developments on the study of i-quantum groups. Precisely, we will establish the geometric Schur-Weyl duality and Howe duality for i-quantum groups, and give the Beilinson-Lusztig-MacPherson realization for i-quantum groups and their canonical basis. The talk is based on a series of joint work with Wang (王伟强), Fan（樊赵兵）, Li （李毅强）, Lai（赖俊儒）, Cui（崔为登） and so on.