In this talk, we shall discuss the asymptotic growth of the Mordell–Weil ranks and the Tate–Shafarevich groups of an elliptic curve E defined over the field of rational numbers. Our focus lies on the behavior along the anticyclotomic Zp-extension of an imaginary quadratic field K, where p is a prime at which E has good supersingular reduction. We shall review the definition and properties of the plus and minus Selmer groups from Iwasawa theory, and explain how to extract arithmetic information of an elliptic curve from these groups.