Abstract: The idea of constructing cohomology classes using congruences between modular forms dates back to the proof of the converse part of the Herbrand-Ribet theorem. We begin by reviewing Ribet's method and its application to the classical Hida family of Eisenstein series. Next, we discuss how applying this method to the Coleman family that is perpendicular to the Hida family suggests the existence of an Euler system. This phenomenon can be further generalized using insights from the p-adic local Langlands correspondence. Finally, we present our work on the construction of an anticyclotomic Euler system for CM fields and its application to the Iwasawa main conjecture.