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The collapse of the World Trade Center (WTC) Towers during the terrorist attacks on September 11, 2001, remains one of the most tragic catastrophes in the field of structural engineering. This paper first reviews a mathematical model that explains the process of the total collapse of the Twin Towers and shows that the downward collapse progression below the impacted floors was spontaneous. The model is based on a continuum description of the motion of the crush front and captures various types of energy dissipation during the collapse. The predictions of this model match all the observations, including the video records of the first few seconds of motion of both towers, the seismic records of the collapse durations for both towers, the mass and size distributions of comminuted concrete particles, and the fast expansion of dust clouds during collapse with the booms generated. This catastrophe provoked general interest in other types of progressive collapse of buildings. This is the subject of the second part of this paper, in which a three-dimensional stochastic computational model for the collapse of RC frame buildings is presented. The occurrence probabilities of different collapse patterns are predicted. The model is further extended to investigate the delayed collapse behavior of RC frames. The results of the analysis shed light on the emerging trend of probabilistic analysis and design of structures against progressive collapse. [ABSTRACT FROM AUTHOR]