Abstract: Stochastic dynamic response and reliability analysis is of paramount importance to guarantee the safety of engineering structures subjected to disastrous dynamic actions. In the past decades, great efforts have been devoted to this field, yielding important progress. However, the stochastic dynamic response analysis and reliability evaluation of MDOF nonlinear systems are still challenging. The probability density evolution method provides a new perspective to this end. In the present paper, the new advances of the probability density evolution method and its applications to seismic response and global reliability of structures, as well as the existing approaches, are outlined and reviewed.