Out-of-time-order correlators (OTOCs) have become a widely-appreciated tool to measure the correlation build-up in space and time, and hence quantitatively characterize information scrambling in interacting many-body systems. Started off as a theoretical tool to understand quantum information in a black hole its impact quickly expanded to a wide variety of subjects including quantum chaos, many-body localization, quantum integrability and recently symmetry-breaking quantum phase transitions. After giving a short introduction to information scrambling and out-of-time-order correlators, I will talk about the emergent relation between symmetry breaking quantum phase transitions and the information scrambling. I will introduce a new theoretical tool to study the physics encoded in an OTOC: dynamical decomposition method. I will show how this tool lets us analytically see the reasons and the mechanism of dynamical detection of symmetry-broken quantum phases via OTOCs. Based on the studies in literature and our numerical results in XXZ-model, our method seems to be universal in explaining the reasoning behind the relation between scrambling and the quantum criticality. If time permits, I will talk about an interesting numerical observation that led us to find a relation between the topological order (in 1D superconductor) at zero temperature and the OTOCs at infinite temperature.