Probing the electroweak phase transition at the LHC and beyond

Uncovering the nature of the electroweak (EW) phase transition in the early Universe would be key to shed light on the origin of the cosmic matter-antimatter asymmetry, and on the cosmological history of the Higgs vacuum. I will discuss searches for new physics beyond the Standard Model at the LHC as a probe of the EW phase transition, as well as the prospects for future colliders such as FCC-ee/hh and CLIC. I will also discuss their complementarity to gravitational wave searches with the future space-based observatory LISA, which will directly access the EW epoch of the early Universe.