We review the theory of cosmic ray transport and acceleration with an emphasis on the underlying plasma physics and examine how that theory can be applied to sources such as supernova remnants and giant radio galaxies. Starting with Fermi's original model for scattering off moving magnetized clouds, we discuss quasilinear transport theory and its application to the acceleration of particles at shock fronts. We discuss problems of injection and the excitation of MHD turbulence by the accelerated particles. In the diffusive limit and at strong shocks this mechanism produces a differential energy spectrum of N(E) ∝ E−2. Recent observations of supernova remnants suggest that their spectra may be steeper than this value. We discuss the transport and acceleration of energetic particles in highly correlated magnetic field structures. In this case particles have an enhanced probability of escape from the shock as they are trapped on field lines and the resulting spectrum is steepened up to a value of 2.5. Fast particle transport also seems to be required by observations of the structures of giant radio galaxy lobes as a function of frequency.