Title: Transseries and Hardy Fields.
Abstract: This will be a survey of our work in the last ten years on these topics. No familiarity with transseries or Hardy fields is required, but I mention here that both are natural settings for solving ordinary differential equations and studying their asymptotics (and for much more). Transseries are formal objects, and Hardy fields consist of actual functions (or rather germs of such). Around 2015 we showed that the differential field of transseries has a good model theory. More recently we showed that sufficiently rich Hardy fields have the same (complete) model theory.