  We consider the propagation of cosmic rays in turbulent magnetic fields. We
use the models of magnetohydrodynamic turbulence that were tested in numerical
simulations, in which the turbulence is injected on large scale and cascades to
small scales. Our attention is focused on the models of the strong turbulence,
but we also briefly discuss the effects that the weak turbulence and the slab
Alfv\'enic perturbations can have. The latter are likely to emerge as a result
of instabilities with in the cosmic ray fluid itself, e.g., beaming and
gyroresonance instabilities of cosmic rays. To describe the interaction of
cosmic rays with magnetic perturbations we develop a non-linear formalism that
extends the ordinary Quasi-Linear Theory (QLT) that is routinely used for the
purpose. This allows us to avoid the usual problem of 90 degree scattering and
enable our computation of the mean free path of cosmic rays. We apply the
formalism to the cosmic ray propagation in the galactic halo and in the Warm
Ionized medium (WIM). In addition, we address the issue of the transport of
cosmic rays perpendicular to the mean magnetic field and show that the issue of
cosmic ray subdiffusion (i.e., propagation with retracing the trajectories
backwards, which slows down the diffusion) is only important for restricted
cases when the ambient turbulence is far from what numerical simulations
suggest to us. As a result, this work provides formalism that can be applied
for calculating cosmic ray propagation in a wide variety of circumstances.
