Wood and composite characterization by the use of mechanical waves is the aim of the works presented. This characterization is achieved by the union of several scientific disciplines: Physics of elastic waves, wood science, signal processing, applied mathematics, statistics, and physical measurements. From a fundamental point of view, it comes then to understand the wave-matter interaction by the direct problem resolution: knowing the state of the physical object and the initial wave impulse, am I able to determine the dynamic response of the object? Then to characterize material properties or to identify heterogeneities by solving the inverse problem: knowing the initial wave impulse and the dynamic response of the material object, am I able to know the state of the object? The discussed problem has multiple facets. Each case of non-destructive testing is in fact unique and how to resolve depends on both the object itself and its context (industrial or scientific). There are also several resolution methods that are sometimes only in common the physics of elastic wave and the object itself (as well as it is possible to solve a problem in very different ways). The works presented are organized as: the characterization of one-dimensional and two-dimensional imaging, the acoustic and ultrasonic waves, the qualitative and quantitative determinations. The results allow exposing the key achievements and some approaches still to explore. The dynamic response can be defined by its spectrum in frequency, by the evolution of this spectrum in time or by a small number of descriptors summarizing vibratory information. The use of statistical methods was necessary to link this information to the intrinsic properties. From this point of view, a spectrum of absorbance in near-infrared spectroscopy is similar to a spectrum of acoustic vibration; the same numerical methods can be used.
