Abstract: For the past few years I have been working on a project to show that the (ordered valued differential) field of logarithmic transseries, $\mathbb{T}_{\log}$, has a good model theory (model completeness, QE, etc). The first part of this project was to show that the asymptotic couple (=value group + additional structure induced by the derivation) has a good model theory. After completing this first part, for the past year I have turned my attention to the field $\mathbb{T}_{\log}$ itself. This project is very similar to the recent results of Aschenbrenner, van der Hoeven and van den Dries in showing that the (ordered valued differential) field of logarithmic-exponential transseries, $\mathbb{T}$, has a good model theory. In this talk I will describe recent progress in the direction of proving model completeness for this structure, as well as the general strategy moving forward. I will also draw parallels between the two fields $\mathbb{T}$ and $\mathbb{T}_{\log}$ to illustrate the obstructions in $\mathbb{T}_{\log}$ that are not present in $\mathbb{T}$.