Phononic crystals are periodic composite materials with lattice spacings comparable to the acoustic wavelength. They are of interest not only because of the profound effects of their periodic structure on wave propagation (e.g., the existence of acoustic band gaps), but also because of potential applications (e.g., their possible role in sound filters, transducer design and acoustic mirrors). In this paper, we summarize recent progress using ultrasonic experiments to investigate both two- and three-dimensional phononic crystals. By measuring the ultrasonic wave field transmitted through slab-shaped samples of different thicknesses, both the dispersion curves and amplitude transmission coefficient can be-determined. Because the field is pulsed, the dynamics of the wave fields can also be investigated; this has allowed us to make a systematic study of ultrasonic wave tunneling in phononic crystals. New result's on resonant tunneling, focussing and negative refraction phenomena in phononic crystals are also presented. Our data are well explained using Multiple Scattering Theory, giving additional insight into the physical properties and potential applications of these novel materials. (C) 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.