A series of historic events beginning with the Ronan Point apartment building collapse in 1968 and continuing in subsequent decades have shown that buildings designed in compliance with conventional design codes can lack the robustness necessary to withstand localised damage, partial collapse or, in some cases, complete collapse. The variable performance of different building forms has led to increased interest from governmental organisations in ensuring all buildings of significant size possess a minimum level of robustness. The research community have responded to this challenge by advancing the understanding of how structures behave when subjected to localised damage. Regulations and design recommendations have been developed to help ensure a more consistent level of resilience for all framed buildings of significant size and rigorous design approaches have been specified for buildings which are deemed potentially vulnerable to extreme loading events (e.g. vehicle borne improvised explosive devices). This paper summarizes some of the more important progressive collapse events in order to identify key attributes that lead to vulnerability to collapse. Current procedures and guidelines for ensuring a minimum level of performance are reviewed and the modelling methods developed for structures subjected to localised damage are described. These include increasingly sophisticated progressive collapse analysis procedures, starting with linear-static and non-linear static analysis and moving through to non-linear static pushover and linear dynamic methods. Finally the fully non-linear dynamic methods are considered. Building connections potentially represent the most vulnerable structural elements in steel framed buildings and their failure can lead to progressive collapses. Steel connections also present difficulties with respect to frame modelling and this paper highlights benefits and drawbacks of some modelling procedures with respect to their treatment of connections.