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Spontaneous symmetry breaking is the foundation of electroweak unificationand serves as an integral part of the model building beyond the standard modelof particle physics and it also finds interesting applications in the lateUniverse. We review development related to obtaining the late cosmicacceleration from spontaneous symmetry breaking in the Universe at largescales. This phenomenon is best understood through Ginzburg-Landau theory ofphase transitions which we briefly describe. Hereafter, we present elements ofspontaneous symmetry breaking in relativistic field theory. We then discuss the"symmetron" scenario-based upon symmetry breaking in the late Universe which isrealized by using a specific form of conformal coupling. However, the model isfaced with "NO GO" for late time acceleration due to local gravity constraints.We argue that the problem can be circumvented by using the massless $\lambda\phi^4$ theory coupled to massive neutrino matter. As for the early Universe,spontaneous symmetry breaking finds its interesting applications in the studyof electroweak phase transition. To this effect, we first discuss in detail,the Ginzburg-Landau theory of first order phase transitions and then apply itto electroweak phase transition including technical discussions on bubblenucleation and sphaleron transitions. We provide a pedagogical expositions ofdynamics of electroweak phase transition and emphasize the need to go beyondthe standard model of particle physics for addressing the baryogenesis problem.Review ends with a brief discussion on Affleck-Dine mechanism and spontaneousbaryogenesis. Appendixes include technical details on essential ingredients ofbaryogenesis, sphaleron solution, one loop finite temperature effectivepotential and dynamics of bubble nucleation.

Spontaneous symmetry breaking in the late Universe and glimpses of early Universe phase transitions \`a la baryogenesis