In this talk I will describe a new result which determines the structure of Galois modules which arise from Kummer theory. More precisely, I will describe a cohomological obstruction for the existence of cyclic sub-modules which is reminiscent of Hilbert's Theorem 90. I will also describe a so-called ``automatic-realization'' result for Galois groups which show how to construct meta-abelian Galois groups from smaller abelian-by-central Galois groups. This is joint work with Minác and Swallow.