We will begin with a general discussion of so-called "pseudo-null" modules over the rings of interest in this talk (namely, formal power series rings over the p-adic integers). The specific modules that we plan to discuss were first studied in Iwasawa's classical theory about the behavior of ideal class groups in certain towers of number fields. We will discuss various questions and conjectures about these modules and recent attempts to say something nontrivial about their structure. In particular, we will describe recent joint work with F. Bleher, T. Chinburg, M. Kakde, R. Sharifi, and M. Taylor.