The topic of progressive collapse of structures has increasingly received particular consideration over recent years, with numerous studies of various forms seeking to explore the complex mechanics of the problem and define ways of minimising its effects. Through a continuing research programme at Imperial College London, considerable advance has been made in understanding the physical features of the progressive collapse response of frame structures, identifying the role of the several different controlling parameters and compiling simplified methods for simulating particular effects. Knowledge of the subject has therefore improved to a considerable extent, that it is now possible to make quantitatively justified assessments of structural robustness by specifying the reasons why a structure might be susceptible to progressive collapse as well as to identify potential methods for enhancing performance. The present paper reviews previous developments at Imperial, evaluates information obtained from relevant experimental studies conducted by other research groups and assesses the progress made both in developing a scientific understanding of the subject and establishing improved ways of tackling the problem in practice. Several factors that should be considered in the robustness design of steel and composite frame structures are defined, and needs for further research into specific aspects of the problem are identified.