The thermal history of the Higgs boson and its connection with electroweak symmetry breaking play an important role in the production of cosmological relics. In this thesis, I study different patterns of the electroweak symmetry at finite temperatures to build a bridge connecting particle cosmology, Higgs phenomenology and physics beyond the Standard Model, that may provide answers to some of the open questions in particle physics. I carefully scrutinize the experimental probes, e.g. measurements of the properties of the Higgs boson and gravitational wave detection, that can directly or indirectly provide information on the validity of the theories I investigate and their early universe electroweak symmetry behavior. The existence of a strong first order electroweak phase transition in the early universe is a necessary building block of the electroweak baryogenesis mechanism, that can explain the matter-antimatter asymmetry of the universe. I investigate representative extensions of the Standard Model Higgs sector, which allow for a strong first order electroweak phase transition and open opportunities for new Higgs decay channels at colliders. I study the electroweak phase transition dynamics, and the relevance of nucleation in models with an additional singlet, both in theories with SM gauge symmetries and in the case of supersymmetry. I also propose a novel scenario, where the electroweak symmetry remains broken up to very high temperatures, thereby allowing to evade strong experimental bounds from CP violation that otherwise plays important limitations on electroweak baryogenesis scenarios. Dynamics of Higgs field bubbles can directly affect the power spectrum of the gravitational wave signals generated during a strong first order phase transition. I perform a first study of the speed of the Higgs bubble wall, and show that it can be significantly slowed down by friction from particles in the hot plasma with resumed soft and collinear radiations.