Classical Iwasawa theory of elliptic curves along the cyclotomic Z_p extensions of number fields proved extremely
fruitful in the arithmetic of elliptic curves. Hida theory extended this to the Iwasawa theory of families of elliptic modular forms.
This talk shall dwell on some recent results on the Iwasawa theory of elliptic curves and modular forms in the setting of
a family of Z_p extensions that lie in an infinite Galois extension of a number field with Galois group isomorphic to Z_p x Z_p.