The purpose of this research is to study theoretically and experimentally the evolution, transport and decay of coherent and incoherent waves (diffused waves) in random and diffused media. It involves a two-dimensional extension of two highly fruitful NSF sponsored research on one-dimensional coherent wave propagation in random media with applications to acoustic emission source characterization, to acoustic emission receiver calibration and to material characterization through internal friction. The incoherent wave will extend the above to practical materials with pronounced microstructural effects. The results of these studies will add to our understanding on wave propagation in real materials with immediate applications to nondestructive evaluation and acoustic emission techniques.