  The Magellanic Clouds have lost most of their gas during their passage by the
Milky Way, a property that has never been successfully modeled. Here we use
accurate and mesh-free hydrodynamic simulations to reproduce the Magellanic
Stream and the Magellanic Clouds in the frame of a 'ram-pressure plus
collision' model. This model reproduces many of the observed properties of the
HI Stream including most of its density profile along its length and its dual
filamentary structure. Besides this, ram-pressure combined with
Kelvin-Helmholtz instabilities extracts amounts of ionized and HI gas
consistent with those observed. The modeled scenario also reproduces the
Magellanic Bridge, including the offset between young and old stars, and the
collision between the Clouds, which is responsible of the very elongated
morphology of the Small Magellanic Cloud along the line of sight. This model
has solved most of the mysteries linked to the formation of the Magellanic
Stream. The Leading Arm is not reproduced in the current model because it
requires an alternative origin.

Astrophysics of Galaxies