Mixture theories developed in the last years by the authors are reviewed and discussed. Some of the theories represent 3-dimensional elastodynamic phenomena by equivalent 2-dimensional models and are applied to investigate dynamic crack problems in laminated and fiber reinforced media. Composites with constituents obeying a variety of constitutive laws are considered. These include laminated solids with linear isotropic elastic, linear anisotropic elastic, nonlinear elastic, thermoelastic and elastic-viscoplastic laminae. Debonding phenomena and large deformations are also treated. In all of the formulated theories, the appearing interaction terms are determined and related to the constituent material parameters. The proposed theories represent the dynamic response of the considered composites to a good degree of accuracy and are governed by field equations which are suitable for solution by proper numerical methods.