The aim of this document is provide a scientific basis for the selection of the model or models that will be underpinning the envisaged EPyRIS decision support tool in terms of assessing and mapping runoff and/or erosion risk in recently burnt areas under different pre- and post-fire management scenarios. To this end, this document reports on a review of the relevant scientific literature, and provide a state-of-the-art of the modelling of runoff and/or erosion following wildfire and post-fire land management, including emergency stabilization measures aiming to reduce runoff and/or the associated soil (fertility) losses.