Abstract 

Birch and Swinnerton-Dyer conjecture is one of the most famous and important problem in pure math, which predicts deep relations between several invariants of elliptic curves defined over number fields. In 1980s, Beilinson, Bloch, and Kato proposed a vast generalization of this conjecture to motives over number fields. In this talk, we will survey results in recent years concerning Beilinson-Bloch-Kato conjectures, and explain major ingredients in their proofs.