  Frequent supernova explosions in compact starburst regions are a main shaper
of these regions' interstellar media (ISM). In most starbursts, the supernova
remnants blast open a hot phase that fills the regions and launches a
superwind. Denser starbursts are too overpressured for hot wind formation, but
supernovae still stir up the ISM. I argue that supernovae power ubiquitous
turbulence through each of the starburst ISM phases, including the hot wind,
and that a fluctuation dynamo amplifies magnetic fields until they are in
equipartition with the turbulence. Supernovae can drive turbulence with speeds
of ~1000 km/s in the hot wind and ~20 km/s in the cold molecular gas, depending
on the outer scale. I predict magnetic field strengths of 70 muG in the
Galactic Center starburst, 300 muG in M82 and NGC 253, and 2 mG in Arp 220's
nuclei. The mean magnetic field strengths are a few times stronger in molecular
gas than in hot winds, but do not vary strongly with density within a
starburst. I explain how the dominance of supernova-driven turbulence leads to
near equipartition between the components of starburst ISM. I also consider
implications for cosmic ray (CR) diffusion in starbursts. The high amounts of
power cascading to small scales could confine CRs very effectively in
starbursts, so much that CR transport is dominated by the flow of gas rather
than diffusion through the gas. In addition, I discuss the effects of
turbulence on X-ray line width, the far-infrared--radio correlation, observed
radio polarization, and Faraday rotation measures. Finally, I discuss the many
questions raised regarding the physics of turbulence in starbursts.
