  Turbulence is ubiquitous in astrophysics. It radically changes many
astrophysical phenomena, in particular, the propagation and acceleration of
cosmic rays. We present the modern understanding of compressible
magnetohydrodynamic (MHD) turbulence, in particular its decomposition into
Alfv\'en, slow and fast modes, discuss the density structure of turbulent
subsonic and supersonic media, as well as other relevant regimes of
astrophysical turbulence. All this information is essential for understanding
the energetic particle acceleration that we discuss further in the review. For
instance, we show how fast and slow modes accelerate energetic particles
through the second order Fermi acceleration, while density fluctuations
generate magnetic fields in pre-shock regions enabling the first order Fermi
acceleration of high energy cosmic rays. Very importantly, however, the first
order Fermi cosmic ray acceleration is also possible in sites of magnetic
reconnection. In the presence of turbulence this reconnection gets fast and we
present numerical evidence supporting the predictions of the Lazarian &
Vishniac (1999) model of fast reconnection. The efficiency of this process
suggests that magnetic reconnection can release substantial amounts of energy
in short periods of time. As the particle tracing numerical simulations show
that the particles can be efficiently accelerated during the reconnection, we
argue that the process of magnetic reconnection may be much more important for
particle acceleration than it is currently accepted. In particular, we discuss
the acceleration arising from reconnection as a possible origin of the
anomalous cosmic rays measured by Voyagers as well as the origin cosmic ray
excess in the direction of Heliotail.
