Flares and coronal mass ejections (CMEs) are more energetic than any other class of solar phenomena. These events involve the rapid release of up to 1033 erg of magnetic energy in the form of particle acceleration, heating, radiation, and bulk plasma motion. Displaying much larger energies, their stellar counterparts are expected to play a fundamental role in shaping the evolution of activity and rotation, as well as the environmental conditions around low-mass stars. While flares are now routinely detected in multi-wavelength observations across all spectral types and ages, direct evidence for stellar CMEs is almost non-existent. In this context, numerical simulations provide a valuable pathway to shed some light on the eruptive behavior in the stellar regime. In this talk, I will review recent results obtained from realistic modeling of CMEs in active stars. Emphasis will be given to M dwarfs, focusing on possible observable coronal signatures of these events using next-generation X-ray missions. Furthermore, an explanation for the lack of Type II radio bursts from CMEs in active M dwarfs despite their frequent flaring will be discussed. Finally, the implications and relevance of these numerical results will be considered in the context of future characterization of host star-exoplanet systems.