In this talk, I describe recent progress in understanding the background field dynamics of the non-relativistic string theory pioneered by Gomis and Ooguri. Building on earlier developments, I present a non-Lorentzian supergravity theory and explain how it constrains the dynamics of the background fields. Special attention will be given to the exotic geometric structures that arise in this theory. I will compare the results with those coming from beta function calculations. In the final part of my talk, I will comment on non-Lorentzian T-duality and an intriguing relation with double field theory.