Currently, the use of numerical models for reproducing the landscape evolution of a river basin is part of the day-by-day research activities of fluvial engineers and geomorphologists. However, despite landscape modelling is based on a rather long tradition, and scientists and practitioners are trying to schematize the processes involved in the evolution of a landscape since decades, there is still the need for improving both the knowledge of the physical mechanisms and their numerical coding. The present review focuses on the first aspect, discussing the main components of a landscape evolution model and their more common schematizations, presenting possible open questions to be addressed towards an improvement of the reliability of such kind of models in describing the fluvial geomorphology.