  We discuss a new type of dust acceleration mechanism that acts in a turbulent
magnetized medium. The magnetohydrodynamic (MHD) turbulence can accelerate
grains through resonant as well as nonresonant interactions. We show that the
magnetic compression provides higher velocities for super-Alfvenic turbulence
and can accelerate an extended range of grains in warm media compared to
gyroresonance. While fast modes dominate the acceleration for the large grains,
slow modes can be important for sub-micron grains. We provide comprehensive
discussion of all the possible grain acceleration mechanisms in interstellar
medium. We show that supersonic velocities are attainable for Galactic dust
grains. We discuss the consequence of the acceleration. The implications for
extinction curve, grain alignment, chemical abundance, etc, are provided.
