Combining quantum many-body physics and nonequilibrium physics is an important opportunity and challenge for current physics research. Nonequilibrium quantum many-body physics is not only a subject of common interest to many branches of physics but also an indispensable theoretical foundation for developing emergent quantum technologies. Cold atom system provides an ideal platform for studying nonequilibrium quantum many-body physics. The advantages of cold atom system, as well as other synthetic quantum systems, are reflected in studying various nonequilibrium processes such as the thermalization of isolated system, dissipation induced by coupling to the environment, ramping, quench, or periodically driving physical parameters of a system. In this work, three examples from our research are discussed to show how the study of nonequilibrium quantum many-body physics with cold atoms can help us go beyond the existing framework of topological physics, uncover new methods of detecting quantum many-body correlations, and enrich the physical content of gauge theory. Such a research concerns the fundamental properties of quantum many-body system, such as topology and correlation, utilizes the advantages of cold atomic system to achieve a quantitative comparison between theory and experiment, and aims at discovering universal physical rules for nonequilibrium quantum many-body process, which can be extended to condensed matter and nuclear matter systems.