In the first half of this talk, we would like to give an overview of Iwasawa theory for elliptic curves and present a pair of p-adic L-functions that serves conveniently in formulating this theory for the supersingular (this adjective will be defined) case. The second half is dedicated to BSD: The classical conjectures of Birch and Swinnerton-Dyer relate the behavior of the Hasse-Weil L-function of an elliptic curve to its Q-rational points. For primes of good reduction, there are p-adic analogues of these conjectures due to Mazur,Tate, and Teitelbaum (ordinary case), and due to Bernardi and Perrin-Riou (supersingular case). The pair of p-adic L-functions can be used to rewrite (and thus unite) their conjectures.