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Recent progress in the use of ultrasonic experiments and Multiple Scattering Theory to investigate wave transport in three-dimensional phononic crystals is summarized. Through appropriate choice of material properties, complete band gaps can be realized for acoustic or elastic waves in such structures. This has allowed us to demonstrate the tunnelling of ultrasound through the band gap and to explore the unexpected effect of absorption on evanescent waves in crystals. Wave propagation above the gap has also been investigated, where we have shown that anisotropy of the wave speeds leads to the focusing of ultrasound without the curved surfaces usually employed in lenses. These ultrasonic experiments and their interpretation using Multiple Scattering Theory illustrate the important contribution that the study of phononic crystals can make to learning about wave scattering and transport in ordered mesoscopic materials.