The quantification of wildfire regimes, especially the relationship between the frequency with which events occur and their size, is of particular interest to both ecologists and wildfire managers. Recent studies in cellular automata (CA) and the fractal nature of the frequency-area relationship they produce has led some authors to ask whether the power-law frequency-area statistics seen in the CA might also be present in empirical wildfire data. Here, we outline the history of the debate regarding the statistical wildfire frequency-area models suggested by the CA and their confrontation with empirical data. In particular, the extent to which the utility of these approaches is dependent on being placed in the context of self-organized criticality (SOC) is examined. We also consider some of the other heavy-tailed statistical distributions used to describe these data. Taking a broadly ecological perspective we suggest that this debate needs to take more interest in the mechanisms underlying the observed power-law (or other) statistics. From this perspective, future studies utilizing the techniques associated with CA and statistical physics will be better able to contribute to the understanding of ecological processes and systems.