Diffusing Acoustic Wave Spectroscopy (DAWS) is an ultrasonic technique that has been developed to measure the dynamics of heterogeneous media from the temporal fluctuations of multiply scattered waves. This technique is similar to more recent developments in field fluctuation spectroscopy, called coda wave interferometry, that use variations in the seismic coda to infer changes in the medium with time. After reviewing the basic principles on which Diffusing Acoustic Wave Spectroscopy is based [M. L. Cowan, J. H. Page, and D. A. Weitz, Phys. Rev. Lett. 85, 453 (2000); Phys. Rev. E 65, 066605 (2002)], its potential as a sensitive method for probing the dynamics of strongly scattering materials will be illustrated with recent experiments on fluidized suspensions of particles. In this type of system, DAWS measures the local relative motion of the scatterers (or strain rate) on a length scale determined by the transport mean free path of the multiply scattered waves. When combined with the complementary technique of Dynamic Sound Scattering using singly scattered waves, DAWS can also determine the instantaneous velocity correlation length of the moving scatterers, thus giving a quite complete picture of the system dynamics over a wide range of length and time scales.