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Nondestructive testing is moving from being an art to a quantitative science. The paper first reviews the ultrasonic NDT literature; this is followed by consideration of the contribution which can be made to the understanding of analytically intractable wave-defect interaction problems by the use of numerical modelling based on explicit finite-difference schemes. Examples are presented of a developing family of ultrasonic NDT techniques which extract additional information from the wave field by combining time-of-flight and mode conversion information with ultrasonic spectroscopy. Immersion schemes, based on leaky Rayleigh waves for surface and near-surface defects are considered. These techniques are shown to extend the scope of ultrasonic NDT with improved reliability of detection and the potential to provide quantitative defect characterisations.