  Multi-dimensional fluid flow plays a paramount role in the explosions of
massive stars as core-collapse supernovae. In recent years, three-dimensional
(3D) simulations of these phenomena have matured significantly. Considerable
progress has been made towards identifying the ingredients for shock revival by
the neutrino-driven mechanism, and successful explosions have already been
obtained in a number of self-consistent 3D models. These advances also bring
new challenges, however. Prompted by a need for increased physical realism and
meaningful model validation, supernova theory is now moving towards a more
integrated view that connects multi-dimensional phenomena in the late
convective burning stages prior to collapse, the explosion engine, and mixing
instabilities in the supernova envelope. Here we review our current
understanding of multi-D fluid flow in core-collapse supernovae and their
progenitors. We start by outlining specific challenges faced by hydrodynamic
simulations of core-collapse supernovae and of the late convective burning
stages. We then discuss recent advances and open questions in theory and
simulations.
