In recent years, advances in computational power have led to an increase in attempts to model the behaviour of wildland fires and to simulate their spread across the landscape. The present series of articles endeavours to comprehensively survey and précis all types of surface fire spread models developed during the period 1990–2007, providing a useful starting point for those readers interested in recent modelling activities. The current paper surveys models of a physical or quasi-physical nature. These models are based on the fundamental chemistry and physics, or physics alone, of combustion and fire spread. Other papers in the series review models of an empirical or quasi-empirical nature, and mathematical analogues and simulation models. Many models are extensions or refinements of models developed before 1990. Where this is the case, these models are also discussed but in much less detail.