Abstract: I will report on recent results obtained in joint work with Anna Rzepka and Steven Dale Cutkosky, in particular some that have connections with the paper by Franziska Jahnke and Konstantinos Kartas that has just been published on arXiv. Building on our paper "The valuation theory of deeply ramified fields and its connection with defect extensions" that has just appeared in the Transactions AMS, we are now working on the following subjects: 1) Galois extensions of prime degree of (roughly) deeply ramified fields can only admit one type of defect, which we call "independent". In an essentially completed follow-up paper we give various characterizations of independent defect. One of them uses Kähler differentials. We also study the special form of these characterizations when the valued field has rank 1 (as perfectoid fields do). 2) In their book "Almost ring theory", Gabber and Ramero use Kähler differentials to characterize deeply ramified fields. In a second paper in preparation, we give a down-to-earth proof of their result by developing tools for the explicit computation of Kähler differentials and then computing them for all possible types of Galois extensions of prime degree of valued fields. If time permits, I will also comment on some aspects of the model theory of roughly tame and roughly Kaplansky fields.