This article presents a review of some important new results on the pr
oblem of cosmic ray propagation and acceleration in interstellar, circ
umstellar, and interplanetary space, taking into account existing inho
mogeneity, anisotropy, and gyrotropy, and also the stochastic properti
es of cosmic media. A unified theoretical method is applied to describ
e cosmic ray distribution. The possibility of a significant decrease i
n cosmic ray diffusivity in compressible turbulent cosmic media is dem
onstrated and discussed. Theoretical results are compared with observa
tions, and some conclusions are drawn on the processes of cosmic ray a
cceleration and propagation.