The role of modelling and in particular numerical modelling of geodynamic processes occurring on geologic timescales is rapidly growing in geosciences (and has a huge potential). State-of-the-art geodynamic models often have a large number of adjustable parameters, which allow fitting of geological, geophysical and geochemical constraints but do not necessarily prove their validity and uniqueness. Current challenges in long-term geodynamic modelling are therefore twofold. On the one hand, a better understanding of the underlying physics of geodynamic processes is required to build realistic predictive models. On the other hand, advances are required in making model results more useable for other areas of geosciences. The purpose of this session is therefore: (a) To compare the results of numerical models with observations from lithospheric-scale to whole-mantle scale. (b) To discuss the more technical aspects of modelling of geodynamic processes (including new numerical techniques and comparison of different numerical approaches). (c) To enhance our understanding of the physics of long-term geological and geodynamic processes (e.g. by combining numerical experiments with analytical insights). (d) To discuss ways to make model results more easily accessible to other disciplines (e.g. by computing synthetictomographic models, gravity anomalies, seismic anisotropy).