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 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. The present paper surveys models of a simulation or mathematical analogue nature. Most simulation models are implementations of existing empirical or quasi-empirical models and their primary function is to convert these generally one-dimensional models to two dimensions and then simulate the propagation of a fire perimeter across a modelled landscape. Mathematical analogue models are those that are based on some mathematical concept (rather than a physical representation of fire spread) that coincidentally represents the spread of fire. Other papers in the series survey models of a physical or quasi-physical nature, and empirical or quasi-empirical nature. Many models are extensions or refinements of models developed before 1990. Where this is the case, these models are also discussed but much less comprehensively.