A cosmological first-order phase transition would have given rise to a stochastic gravitational wave background which may be observable today. Phase transitions are driven by thermal loop fluctuations, which modify background fields at leading order. This breaks the usual loop expansion and leads to large theoretical uncertainties in typical calculations, especially for gravitational wave predictions. I will give an overview of our present understanding of these uncertainties, and of the tools that have been developed to overcome them. Effective field theory has been at the forefront of this development, and I will outline how it solves a number of long-standing theoretical problems.
 
https://indico.ijs.si/event/1551/