Recent work of Greenberg and Vatsal studies the relationship between the Iwasawa invariants of Selmer groups attached to modular forms that are congruent modulo a prime p, viewed over the cyclotomic Z_p-extension. I will discuss a related picture in the context of Rankin L-series attached to a modular form and an imaginary quadratic field, and the many open questions that arise naturally in the context of this study.