In this talk, I will briefly talk about classical Iwasawa theory and the Iwasawa theory of (fine) Selmer groups of Abelian varieties.

Following this introduction, I will explain the growth of the fine Selmer group in towers of number fields and relate it to the growth of class groups in such towers.

This which will show the close relationship between the classical Iwasawa theory and the Iwasawa theory of Abelian varieties.

Finally, I will report on some modest progress made towards some of these conjectures.

Some parts of this talk is joint work with R. Sujatha.