I shall relate the modern understanding of MHD turbulence with the basic processes of cosmic ray propagation and acceleration. First of all, I shall show that on the scales less than the turbulence injection scale, which is approximately 100 pc for the Milky Way, cosmic rays undergo super diffusion in the direction perpendicular to the mean galactic magnetic field. Then I will show how turbulence damping of the streaming instability depends on the regime of turbulence, e.g. strong Alfvenic or weak Alfvenic turbulence, and what are the astrophysical consequences of this instability. In particular, I shall show that the in the Galactic halo the weak turbulence and not strong turbulence is responsible for the damping of the streaming instability. Finally, I shall discuss how these two processes affect cosmic ray acceleration in shocks.