An Euler system is a family of cohomology classes that satisfy some compatibility condition under the corestriction map. Kato constructed an Euler system for a modular form over the cyclotomic extensions of Q. I will explain a recent joint work with David Loeffler and Sarah Zerbes where we generalize Kato's work to construct an Euler system for the Rankin-Selberg convolution of two modular forms. I will also explain how a similar construction is possible for a modular form over ray class fields of an imaginary quadratic field.