One of the primary formation channels for compact object binaries, including progenitors of gravitational-wave sources, critically depends on a violent phase of binary star interaction known as common envelope evolution (CEE). During this phase, the system undergoes rapid loss of mass, angular momentum, and energy. Despite its central importance in binary evolution, CEE remains one of the most challenging and poorly understood problems in stellar astrophysics, with most observational constraints coming indirectly from progenitor or remnant systems. Recent studies have linked the dynamical phase of CEE to a class of optical transients known as Luminous Red Novae (LRNe), which are characterized by slow outflows and efficient formation of dust and molecules. In this talk, I will provide an overview of CEE and present recent results that shed light on its dynamics using 1D semi-analytic models, as well as 2D and 3D radiation- and magnetohydrodynamical simulations.