The method of finite support iterations with fams (finitely additive measures) on the power set of the natural numbers was first developed by Saharon Shelah (2000) to construct a model of ZFC where the cofinality of the covering of measure is countable. This type of iterations, as well as iterations with ultrafilter-limits, has played a fundamental role in recent work about the consistency of Cichon's maximum (with Kellner, Goldstern, and Shelah, also with Tanasie).
In this talk, I present recent progress and generalizations of the technique of iterations with ultrafilter-limits and fam-limits, and its effect on some classical cardinal characteristics of the continuum, as developed in joint work with Brendle, Miguel Cardona, and Andrés Uribe-Zapata (as well as in work by Takashi Yamazoe).