Although equilibrium statistical physics has achieved great success, equilibrium systems are an exception rather than the rule. Recent experiments in ultracold atoms have offered a platform for real-time observation of nonequilibrium behavior in quantum phase transitions. Here I shall introduce our recent studies on nonequilibrium universal behavior in critical phenomena that possess a long correclation time. These include nonequilibrium universal quantum critical initial slip in imaginary time for a closed quantum system quenched to its critcal point and our theory of finite-time scaling for driven nonequilibrium critical phenomena and its applications to Kibble-Zurek mechanism and nonequilibrium quantum criticality in an open system.