Non-relativistic strings from WZW theories

String theory, in its most elementary formulation, is a set of maps from a worldsheet to some target space. In the quest for a theory of quantum gravity, our models almost always have Lorentzian target spaces (or backgrounds). However, what happens if we consider non-Lorentzian target spaces? In particular, what about Galilean target spaces? This leads to the notion of non-relativistic strings, which have become much more popular in the last 10 years for various reasons. However, there are exceedingly few explicit examples of non-relativistic strings that one can build as the quantisation of a field theory on a worldsheet. To remedy this, I present my work with my supervisor, which involves building a class of non-relativistic string theories by appropriately gauging certain types of WZW models.