the iwasawa theory of selmer groups provides a natural way for p-adic approach to the celebrated birch and swinnerton dyer conjecture. over a non-commutative p-adic lie extension, the (dual) selmer group becomes a module over a non-commutative iwasawa algebra and its structure can be understood by analyzing ``(left) reflexive ideals'' in the iwasawa algebra. in this talk, we will start by recalling several existing conjectures in iwasawa theory and then we will give an explicit ring-theoretic presentation, by generators and relations, of such iwasawa algebras and sketch its implications in understanding the (two-sides) reflexive ideals. generalizing clozel's work for $sl(2)$, we will also show that such an explicit presentation of iwasawa algebras can be obtained for a much wider class of p-adic lie groups viz. uniform pro-p groups and the pro-p iwahori of $gl(n,z_p)$. further, if time permits, i will also sketch some of my recent iwasawa theoretic results joint with sujatha ramdorai.