Instabilities of nonuniform flows is a fundamental problem in dynamics of fluids and plasmas. This presentation outlines atypical dynamics of instabilities for unmagnetized and magnetized astrophysical differentially rotating flows, including, our efforts in the development of general theory of magneto rotation instability (MRI) that takes into account plasma compressibility, pressure anisotropy, dissipative and kinetic effects. Presented analysis of instability (transient growth) processes in unmagnetized/hydrodynamic astrophysical disks is based on the breakthrough of the hydrodynamic community in the 1990s in the understanding of shear flow non-normality induced dynamics. This analysis strongly suggests that the so-called bypass concept of turbulence, which has been developed by the hydrodynamic community for spectrally stable shear flows, can also be applied to Keplerian disks. It is also concluded that the vertical stratification of the disks is an important ingredient of dynamical processes resulting onset of turbulence.
