The Coronal Mass Ejections (CMEs) are the most violent manifestations of solar activity. They are huge eruptions of magnetized plasma that are expelled from the solar corona (the upper layer of the Sun's atmosphere) into interplanetary space. When directed towards the Earth, they interact with the Earth's magnetic field causing severe disturbances in the terrestrial magnetosphere, known as geomagnetic storms. The energy released by CMEs in geospace can induce major effects on human activities, either on ground or in space. Predicting CMEs, their time of arrival on Earth, and their geo-effectiveness, namely the intensity of induced geomagnetic storms, is therefore vital. This activity falls within the branch of heliophysics known as "Space Weather", which deals precisely with the study of solar-terrestrial relations. The different forecasting methods proposed so far can be classified into three major categories, namely empirical, drag-based and physics-based models. Recently, new approaches using Artificial intelligence (AI) are gaining increasing popularity in the prediction of geo-effective solar events. In fact, Machine/Deep Learning (ML/DL) techniques are increasingly being employed in Space Weather studies, often performing far better than previous models. This talk explores the physics of solar and magnetospheric processes behind the Space Weather prediction tools developed within the AIxtreme project. REFERENCES [1] Odstrcil, D. (2003). Modeling 3-D solar wind structure. Advances in Space Research, 32(4), 497–506. https://doi.org/10.1016/s0273-1177(03)00332-6 [2] Odstrcil, D., P. Riley, and X. Zhao (2004), Numerical simulation of the 12 May 1997 interplanetary CME event, J. Geophys. Res.,  109, A02116. https://doi.org/10.1029/2003JA010135 [3] Pomoell, J., & Poedts, S. (2018). EUHFORIA: European heliospheric forecasting information asset. Journal of Space Weather and Space Climate, 8, A35. https://doi.org/10.1051/swsc/2018020 [4] Schwenn, R. (2006). Space weather: The solar perspective. Living Reviews in Solar Physics, 3(1), 2. https://doi.org/10.12942/lrsp-2006-2 [5] Vourlidas, A., Patsourakos, S., & Savani, N. (2019). Predicting the geoeffective properties of coronal mass ejections: Current status, open issues and path forward. Philosophical Transactions of the Royal Society A, 377(2148), 20180096. https://doi.org/10.1098/rsta.2018.0096 [6] Vršnak, B., Žic, T., Vrbanec, D., Temmer, M., Rollett, T., Möstl, C., et al. (2013). Propagation of inte