Solar Coronal Mass Ejections (CMEs) are large-scale eruptive events in which large amounts of plasma (up to 10 13 -10 16 g) and magnetic field are expelled into interplanetary space at very high velocities (typ. 450 km/s, but up to 3000 km/s). When sampled in situ by a spacecraft in the interplanetary medium, they are termed Interplanetary CMEs (ICMEs). They are considered the major drivers of “space weather” and the associated geomagnetic activity. The detectable space weather effects on Earth appear in a broad spectrum of time and length scales and have various harmful effects on human health and the technologies on which we are ever more dependent. Severe conditions in space can hinder or damage satellite operations and communication and navigation systems. They can even cause power grid outages leading to various socio-economic losses. In order to mitigate these effects or at least lower their impact, numerical physics-based models are developed to unravel the physics behind these phenomena and predict the effects a few days in advance.

To predict the impact of a CME and its so-called geo-effectiveness, it is important to take into account the internal magnetic structure of the CMEs as the sign of the magnetic field component perpendicular to the equatorial plane upon arrival at Earth is a key parameter. I will first present the challenges in modelling the solar want and the evolution of CMEs. Then, I will go deeper into the latest results on magnetic flux-rope models for CMEs implemented in EUHFORIA, our heliospheric wind and CME evolution model (Pomoell & Poedts, 2018). These state-of-the-art models include the spheromak model, Fri3D (Flux-Rope in 3D), the radially contracted spheromak, two analytical and self-similar toroidal CME models (based on the Soloviev and Miller-Turner solutions), and a novel ‘horseshoe’ CME model (Maharana et al. 2024). I will also mention our novel modified Titov-Démoulin and RBSL flux- rope CME models that we can launch from the low solar corona via our global MHD coronal model COCONUT (Perri, Leitner et al. 2022). These CME models are integrated into Sun-to-Earth model chains. They are used to predict the geo-effectiveness of CME impacts on Earth, quantified by magnetosphere models and models for Dst, Kp, etc. indices.