It is now more or less well-known that the Euler system method in Iwasawa theory yields the one-sided divisibility of Iwasawa main conjectures and an upper bound of Selmer groups. We discuss how one can numerically check the Euler system method (with Kato’s Euler systems) indeed gives the equality of the main conjecture for modular forms and the exact order of Selmer groups. It includes the joint works with Myoungil Kim and Hae-Sang Sun (for modular forms of weight 2 at good primes), Kentaro Nakamura (for elliptic curves at additive primes).