The possible existence of beyond Standard Model physics at the TeV scale or below has important implications for the thermal history of electroweak symmetry-breaking. A first order phase transition – not possible in the minimal Standard Model with a 125 GeV Higgs boson – would provide the preconditions for electroweak baryogenesis and the generation of primordial gravitational radiation. I discuss recent developments in assessing this possibility that rely on the combination of EFT methods and non-perturbative (lattice) computations. I also discuss implications for high energy collider phenomenology and next generation gravitational wave searches.