Abstract: About 10 picoseconds after the beginning of the Universe, the Higgs field turned on. In extensions of the Standard Model of particle physics, this could have been a first order phase transition, with the spontaneously nucleated bubbles of the Higgs phase expanding and colliding at relativistic speeds.  I will survey ongoing work  to characterise the spectrum of gravitational radiation from early universe phase transitions, prospects for observing the radiation at the future space-based gravitational wave detector LISA, and outline how LISA can complement the LHC as a probe of phase transitions and physics beyond the Standard Model.