Iwasawa theory studies arithmetically significant modules (e.g. class groups and Selmer groups) associated with pro-$p$-extensions $K/k$ of global fields ($p$ a prime). It usually focuses on $p$-parts of such modules and few results are known on $\ell$-parts ($\ell\neq p$ another prime), mainly obtained by means of analytic methods. We present an algebraic approach to study $\ell$-parts as modules over the algebra $\mathbb{Z}_\ell[[\text{Gal}(K/k)]]$, providing structure theorems, characteristic ideals, orders, $\mathbb{Z}_\ell$-ranks and so on. In the case of class groups, such modules naturally verify a theorem of Sinnott on the $p$-adic limit of their orders (or their $\mathbb{Z}_\ell$-ranks when they are not finite). We show that this holds for more general modules and (if time permits) conclude with a (tentative) formulation of a Main Conjecture for this setting. This is joint work with Ignazio Longhi (Torino).