The distinguished properties of stochastic systems in civil structures subjected to dynamic disastrous actions include: (1) Randomness involved in both structural properties, which are essentially random fields, and external dynamic excitations such as strong earthquakes and wind, which are essentially stochastic processes; (2) Strong nonlinearity of restoring force, including strength degradation and stiffness degradation, which could not be described by polynomials and should be captured by the elastoplastic damage mechanics; and (3) Large degrees of freedom in the order of magnitude of millions or larger. The coupling of randomness and nonlinearity in large degrees of freedom systems leads to great difficulty in uncertainty quantification and global reliability of such real-world civil structures, and hinders effective design trading off safety and economical efficiency. In this presentation, the probability density evolution method (PDEM) will be outlined. In this method, by combining the principle of preservation of probability and the underlying physical mechanism, a state variables decoupled generalized density evolution equation (GDEE) could be derived. This equation reveals that the change of probabilistic information of the response is determined by the change of the underlying physical state. The technically most appealing property of this partial differential equation is that the dimension of this equation depends only on the number of quantity of interest, rather than the dimension of the embedded system. Consequently, combining the embedded deterministic analyses, from which the mechanism of propagation of uncertainty is captured, and the solution of GDEE, will lead to instantaneous probability density function of the quantity of interest. The applications to the seismic response and global reliability of real-world civil structures will be exemplified. Challenging problems to be further resolved, as well as most recent advancement, will be discussed.