Hall Effect Thrusters (HETs) are used for satellites applications, particularly orbiting at Low/Geo Earth Orbit (LEO/GEO) for telecommunications and government spacecraft because their efficiency and competitiveness if compared to other electric propulsion devices. Furthermore, HETs have a great potential because, in the future, they could be used for orbit transfers and interplanetary space missions. Computational modelling of plasma in HET has resulted interesting for several reasons. First, it can be used to predict thrusters’ operative life; this feature, indeed, is compromised by the contact of plasma particles with the walls of the device (erosion phenomenon). Secondly, it can help to understand better the physic of these devices; the electron transport across the magnetic field and its coupling with the electric field and the neutral atom density are the phenomena that make complex and non-linear the physics.