Close inspection of accidental fires in large, open-plan compartments reveals that they do not burn simultaneously throughout the whole enclosure. Instead, these fires tend to move across floor plates as flames spread, burning over a limited area at any one time. These fires have been labelled "travelling fires". Current structural fire design methods do not account for these types of fires. Despite these observations, fire scenarios most commonly used for the structural design of modern buildings are based on traditional methods that assume uniform burning and homogenous temperature conditions throughout a compartment, regardless of its size. This paper is Part I of a two part article and is a literature review of travelling fire research.A brief background to the traditional methods that assume uniform fires is given along with critiques of that assumption, such as the heterogeneity of compartment temperatures and the observation of travelling fires in both accidental events and controlled tests. The research in travelling fires is reviewed, highlighting the pioneering work in the field to date. The main challenge in developing tools for incorporating travelling fires into design is the lack of large scale test data. Nonetheless, significant progress in the field has been made and a robust methodology using travelling fires to characterise the thermal environment for structural analysis has been developed. The research in quantifying the structural response to travelling fires is also reviewed.