This is a review of the most important work in wildland fire mathematical modelling which has been carried out at different research centres around the world from the beginning of the 1940s to the present. A generic classification is proposed which allows wildland fire models to be sorted. Surface fire spread models, crown fire initiation and spread models, spotting and ground fire models are reviewed historically and the most significant ones are analysed in depth. The last two sections are dedicated to wildland fire behaviour calculation systems based on the reviewed models. The evolution and complexity of these systems is analysed in parallel with the development of new technologies. Special attention is given to the tools most commonly in current use by forestry agencies. (C) 2003 Elsevier Science Ltd. All rights reserved.