The nature of MHD and hydrodynamical turbulence in accretion disks is discussed. Comparison is made with planar Couette flow, a classical system prone to nonlinear shear instability resulting in enhanced turbulent transport. Both Keplerian and non-Keplerian hydrodynamical disks are studied, and it is found that only constant angular momentum disks are unstable to nonlinear disturbances and develop enhanced turbulent transport. Convective instabilities do not lead to enhanced turbulent transport. Hydrodynamical Keplerian disks are quite stable to nonlinear disturbances. Several lines of argument are presented which all lead to this conclusion, but the key to disk turbulence is the interaction between the stress tensor and the mean flow gradients. The nature of this coupling is found to determine completely the stability properties of disks (hydrodynamics and magnetic), and the nature of turbulent transport. The weak field MHD instability, which is of great astrophysical importance, displays the same type of stress tensor – mean flow coupling that all classical local shear instabilities exhibit. Hydrodynamical Keplerian disks, on the other hand, do not. Accretion disk turbulence is MHD turbulence.