Fugitive methane emissions account for a significant proportion of greenhouse gas emissions, and their elimination by catalytic combustion is a relatively easy way to reduce global warming. New and novel reactor designs are being considered for this purpose, but their correct and efficient design requires kinetic rate expressions. This paper provides a comprehensive review of the current state of the art regarding kinetic models for precious metal catalysts used for the catalytic combustion of lean methane mixtures. The primary emphasis is on relatively low-temperature operation at atmospheric pressure, conditions that are prevalent in the catalytic destruction of low concentrations of methane in emission streams. In addition to a comprehensive literature search, we illustrate a detailed example of the methodology required to determine an appropriate kinetic model and the constants therein. From the wide body of literature, it is seen that the development of a kinetic model is not necessarily a trivial matter, and it is difficult to generalize. The model, especially the dependence on the water concentration, is a function of not only the active ingredients but also the nature of the support. Kinetic modelling is performed for six catalysts, one commercial and five that were manufactured in our laboratory, for illustration purposes.