The knowledge of a free-burning fire's potential rate of spread is critical for safe and effective bushfire control and use. A number of models for predicting the head-fire rate of spread in various types of Australian vegetation have been developed over the past 60 years or so since Alan G. McArthur began his pioneering research into bushfire behaviour. Most of the major Australian vegetation types have had more than one model developed for operational use. These include grassland, shrubland, both dry and wet eucalypt forests, and pine plantation fuel types. A better understanding of the technical basis for each of these models and their utility is essential for the correct selection and application of the most appropriate models. This review provides a systematic overview of 22 models of the rate of fire spread and their applicability in prescribed burning and wildfire operations. Background information and a description of each model is given. This includes information on the data used in the model development that defines the bounds of its application. The mathematical equations that represent each model are given along with a discussion of model form and behaviour, the main input variables and their influence, and evaluations of model performance undertaken to date. This review has enabled the identification of those models that constitute the current state of knowledge with respect to bushfire behaviour science in Australia. We recommend the models that should underpin best practice in the near term in the operational prediction of fire behaviour and those that should no longer be used, and provide reasons for these recommendations.