  Numerical simulations shed light onto earlier not trackable problem of
magnetohydrodynamic (MHD) turbulence. They allowed to test the predictions of
different models and choose the correct ones. Inevitably, this progress calls
for revisions in the picture of cosmic ray (CR) transport. It also shed light
on the problems with the present day numerical modeling of CR. In this paper we
focus on the analytical way of describing CR propagation and scattering, which
should be used in synergy with the numerical studies. In particular, we use
recently established scaling laws for MHD modes to obtain the transport
properties for CRs. We include nonlinear effects arising from large scale
trapping, to remove the 90 degree divergence. We determine how the efficiency
of the scattering and CR mean free path depend on the characteristics of
ionized media, e.g. plasma $\beta$, Coulomb collisional mean free path.
Implications for particle transport in interstellar medium and solar corona are
discussed. We also examine the perpendicular transport of CRs. Perpendicular
transport depends on the comparison of parallel mean free path and the
injection scale of the turbulence, as well as the Alfv\'enic Mach number.
Normal turbulence does not allow subdiffusion unless there are slab waves. The
critical scale below which subdiffusion applies is provided. These results can
be used to compare with the numerical calculations, provided that these
calculations use the structure of magnetic field which is consistent with the
numerical studies of MHD turbulence.
