  Coronal mass ejections (CMEs) are more energetic than any other class of
solar phenomena. They arise from the rapid release of up to $10^{33}$ erg of
magnetic energy mainly in the form of particle acceleration and bulk plasma
motion. Their stellar counterparts, presumably involving much larger energies,
are expected to play a fundamental role in shaping the environmental conditions
around low-mass stars, in some cases perhaps with catastrophic consequences for
planetary systems due to processes such as atmospheric erosion and depletion.
Despite their importance, the direct observational evidence for stellar CMEs is
almost non-existent. In this way, numerical simulations constitute extremely
valuable tools to shed some light on eruptive behavior in the stellar regime.
Here we review recent results obtained from realistic modeling of CMEs in
active stars, highlighting their key role in the interpretation of currently
available observational constraints. We include studies performed on M-dwarf
stars, focusing on how emerging signatures in different wavelengths related to
these events vary as a function of the magnetic properties of the star.
Finally, the implications and relevance of these numerical results are
discussed in the context of future characterization of host star-exoplanet
systems.
