Ultrasonic wave transport in strongly scattering, disordered media is investigated via analysis of the multiply-scattered transmitted field. Measurements of transverse confinement, statistics, and correlations of the intensity were performed on an aluminum mesoglass, where aluminum beads were brazed together to form a porous slab sample. Comparison of the transverse confinement measurements with the self-consistent theory of localization was used to identify and locate a mobility edge in the sample at f = 1.1011 MHz, enabling a measurement of the critical exponent nu characterizing the Anderson transition, nu ~ 1.6–2. Infinite-range C0 correlations were observed, and observed to grow dramatically near the mobility edge, along with the C2 and C3 correlations. Measurements of the multifractal exponent Delta_2 were able to confirm the link between C0 correlations and Anderson localization. Experiments using the aluminum mesoglass with ethanol-filled pores showed evidence of two nearly-independent propagating modes, one of which appears to be characterized by a strongly renormalized diffusion coefficient. The density of states and level spacing statistics were investigated using a different mesoglass, constructed by sintering glass beads percolated on a random lattice. Direct measurements of these quantities were obtained by cutting small samples of this mesoglass, allowing individual vibrational modes to be resolved. The density of states showed a plateau extending well into the expected Debye regime, and evidence of a Boson peak was observed at low frequencies. The level spacing statistics indicated that transport in the frequency ranges measured was on the diffusive side of the mobility edge, showing agreement with the predictions of the GOE from random matrix theory. The dynamics of a suspension of bubbles were investigated using phase-based Diffusing Acoustic Wave Spectroscopy, where phase correlations were found to give additional information beyond traditional field- and intensity-based correlation measurements. / October 2015