The current soot oxidation catalyst scenario has been reviewed, the main factors that affect the activity of powder catalysts have been highlighted and kinetic soot oxidation models have been examined. A critical review of recent advances in modelling approaches has also been presented in this work. The multiscale nature of DPFs lends itself to a hierarchical organization of models, over various orders of magnitude. Different observation scales (e.g., wall, channel, entire filter) have often been addressed with separate modelling approaches that are rarely connected to one another, mainly because of computational difficulties. Nevertheless, DPFs exhibit an intrinsic multi-scale complexity that is reflected by a trade-off between fine and large-scale phenomena. Consequently, the catalytic behavior of DPFs usually results in a non-linear combination of multi-scale phenomena. (C) 2015 Published by Elsevier B.V.