  Cosmic ray (CR) transport and acceleration is essential for many
astrophysical problems, e.g., CMB foreground, ionization of molecular clouds
and all high energy phenomena. Recent advances in MHD turbulence call for
revisions in the paradigm of cosmic ray transport. We use the models of
magnetohydrodynamic turbulence that were tested in numerical simulation, in
which turbulence is injected at large scale and cascades to to small scales. We
shall address the issue of the transport of CRs, both parallel and
perpendicular to the magnetic field and show that the issue of cosmic ray
subdiffusion is only important for restricted cases when the ambient turbulence
is far from that suggested by numerical simulations. Moreover, on scales less
than injection scale of turbulence, CRs's transport becomes super-diffusive. We
also shall discuss the nonlinear growth of kinetic gyroresonance instability of
cosmic rays induced by large scale compressible turbulence. This gyroresonance
of cosmic rays on turbulence is demonstrated an important scattering mechanism
in addition to direct interaction with the compressible turbulence. The
feedback of the instability on large scale turbulence cannot be neglected, and
should be included in future simulations.
