A strong first-order electroweak phase transition provides a possible mechanism to generate baryon asymmetry in the early universe, and it may impact on the thermal environment of dark matter formation and evolution. Also, gravitational wave signals from first-order phase transitions and cosmic strings are important targets of gravitational wave experiments such as PTA, LIGO, LISA, Taiji and Tianqin. In this talk, I will share our recent progress in the study of symmetry breaking in the early universe, including physics of Higgs mechanism, dark matter and gravitational waves.