There is a classical theorem of Iwasawa which concerns certain modules X for the formal power series ring Λ = Zp[[T]] in one variable. Here p is a prime and Zp is the ring of p-adic integers. Iwasawa's theorem asserts that X has no nonzero, finite Λ-submodules. We will begin by describing the modules X which occur in Iwasawa's theorem and explaining how the theorem is connected with the title of my talk. Then we will describe generalizations of this theorem for certain Λ-modules (the so-called "Selmer groups") which arise naturally in Iwasawa theory. The ring Λ can be a formal power series ring over Zp in any number of variables, or even a non-commutative analogue of such a ring.