Non Destructive Testing and Evaluation (NDTE) is addressed starting from the reality of the studied material (steel, concrete, composites, nuclear fuel) and their industrial applications (in-situ constraints). All NDTE techniques (ultrasound, X-ray, eddy current , thermography ... ) are considered before choosing a methodology of study. Research activities revolve mainly around the modeling of materials and appropriate experiments on samples representative of the issues. The ultrasonic waves are often preferred to monitor and characterize the materials; their propagation is studied in order to obtain the desired properties through signal analysis and inverse approaches.