During the entire life cycle, the facilities are experienced to force and environmental actions of various nature and intensity. In some cases, such influences can lead to a loss of the bearing capacity of the structural elements of a building, which in turn can lead to a disproportionate failure of the entire structural system. Such phenomenon was called progressive collapse. Major accidents at facilities, such as the collapse of a section of the Ronan Point high-rise residential building (London, 1968), the Sampoong department store (Seoul, 1995), the Transvaal Park pavement (Moscow, 2004), the World Trade Center (New York, 2011) and others, clearly demonstrated the urgency of this problem. In this regard, the regulatory documents of the USA, Great Britain, EU, China, Australia, Russia and other countries established requirements for the need to calculate structural systems of buildings for resist to progressive collapse after sudden localized structural damage. However, the steady increase in the number of new publications on the problem of progressive collapse observed in the world scientific literature indicates that the results of such studies do not yet provide exhaustive answers to all questions related to this phenomenon. In this regard, the proposed review article is aimed at systematizing, generalizing and analyzing new research results on resistance to progressive collapse of facilities, identifying new trends and proposing new research directions and tasks to improve the level of structural safety of design solutions for buildings and structures. In order to achieve this goal, the following aspects were considered: the nature of the impacts leading to progressive collapse; features of modeling the progressive collapse of structural systems of buildings and structures; mechanisms of resistance to progressive collapse and criteria for evaluation of a progressive collapse resistance. Particular attention in the scientific review is paid to the analysis of works related to a new direction of research in the area under consideration, associated with the assessment of the bearing capacity of eccentrically compressed elements of structural systems, the effect on their resistance to progressive collapse of the parameters of the loading mode, degradation of material properties and the topology of the structural system. The significance of the proposed scientific review is that, along with the well-known and new results presented in the English-language scientific literature, it summarizes and analyzes the original approaches, methods and research results published in Russian-language scientific publications, primarily included in the RSCI Web of Science.