Although design codes and standards of practice are written assuming that the probability of building collapse is low under extreme earthquake shaking, the likelihood of collapse in such shaking is almost never checked. This chapter discusses analytical modeling of component behavior and structure response from the onset of inelastic behavior to lateral displacements at which a structure becomes dynamically unstable. A component model that captures the important deterioration modes observed in steel components is calibrated using data from tests of scale-models of a moment-resisting connection. This connection is used in the construction of two scale models of a modern four-story steel moment frame. The scale models are tested through collapse on an earthquake simulator at the NEES facility at the University at Buffalo. The results of these simulator tests show that it is possible to predict the sidesway collapse of steel moment resisting frames under earthquake shaking using relatively simple analytical models provided that deterioration characteristics of components are accurately described in the models.