This paper summarizes collapse performance measures and the probabilistic basis for their development to assist in understanding of collapse behaviour of buildings and implementation of performance objectives in design and evaluation of buildings for collapse safety. Collapse in this context is defined as the loss of lateral load-resisting capability of a building's structural system caused by ground shaking. Estimation of collapse performance requires the relation between a ground motion intensity measure (IM) and the probability of collapse, denoted as collapse fragility curve, and the relation between the same ground motion IM and the seismic hazard for the building, denoted as seismic hazard curve. Two methods for estimating the collapse fragility curve of a building are discussed: the EDP-based approach and the IM-based approach. In both approaches, collapse is associated with a scalar ground motion IM and is obtained by utilizing Incremental Dynamic Analysis. The collapse performance criteria presented in this paper are compared with the collapse performance criteria recommended in the SAC/Federal Emergency Management Agency guidelines. An eight-storey moment-resisting frame case study is used to compare the estimates of collapse performance of various approaches discussed in this paper. Copyright © 2009 John Wiley & Sons, Ltd.