摘要：We provide a selective overview of the study of leading terms of arithmetic L-functions, ranging from the classical "analytic class number formula" (from the 19th Century) to the Birch and Swinnerton-Dyer Conjecture (from the 1960s) and the extremely general "Tamagawa Number Conjecture" of Bloch and Kato (from the late 1980s). The talk is intended to be accessible to a wide audience and so we heavily focus on underlying ideas and philosophies rather than technical details.