  The mechanism of core-collapse supernova explosions must draw on the energy
provided by gravitational collapse and transfer the necessary fraction to the
kinetic and internal energy of the ejecta. Despite many decades of concerted
theoretical effort, the detailed mechanism of core-collapse supernova
explosions is still unknown, but indications are strong that multi-D processes
lie at its heart. This opens up the possibility of probing the supernova
mechanism with gravitational waves, carrying direct dynamical information from
the supernova engine deep inside a dying massive star. I present a concise
overview of the physics and primary multi-D dynamics in neutrino-driven,
magnetorotational, and acoustically-driven core-collapse supernova explosion
scenarios. Discussing and contrasting estimates for the gravitational-wave
emission characteristics of these mechanisms, I argue that their
gravitational-wave signatures are clearly distinct and that the observation (or
non-observation) of gravitational waves from a nearby core-collapse event could
put strong constraints on the supernova mechanism.
