in iwasawa theory, one attempts to relate arithmetic objects arising from galois cohomology groups to analytic objects, specifically $p$-adic $l$-functions, usually at the level of a cyclotomic $z_p$-extension of a number field. for some time, i have been interested in operations in the galois cohomology of number fields with restricted ramification, particularly cup products. i will explain various applications of these operations, for instance to iwasawa theory over certain nonabelian $p$-adic lie extensions of number fields. i will then discuss the broad outline of a conjecture relating an inverse limit of such cup products up the cyclotomic tower to the two-variable $p$-adic $l$-function for hida families of cusp forms congruent to eisenstein series modulo $p$.