The last decade has been marked by substantial advamces in understanding of the role and properties of astrophysical turbulent magnetic fields. This has induced substancial paradigm shifts for the problem of cosmic ray propagation and acceleration. This book introduces to the reader the mordern understanding of magnetohydrodynamic (MHD) turbulence and describes how the advances in MHD turbulence theory affect the key aspects of particle acceleration and transport in astrophysical environments. The book presents the implications of the improved treatment of cosmic ray dynamics for various problems ranging from particle acceleration in solar flares and the propagation of cosmic rays in the galaxy to powering enigmatic gamma ray bursts. In addition, the book discusses the acceleration of dust grains by MHD turbulence as well as new ways of observational studies of magnetic fields based on ground state alignment. The book should be useful for astrophysics graduate students and anyone interested at the current developments in MHD turbulence theory and its astrophysical implications.