This work focuses on establishing the scientific and engineering foundations for the design and modeling of novel microcellular acoustical polymeric and ceramic foams and gaining a fundamental understanding of the mechanisms and critical parameters governing their sound absorption behavior. The presented research is particularly intended to broaden the knowledge in the fields of understanding the effects of structure and morphology on the acoustical behavior of microcellular foams. In this context, an attempt has been made to establish rigorous, experimentally validated, theoretical models that describe the phenomena and increase the accuracy of the current sound propagation models by integrating the structure and morphology effects to them for better design of acoustical materials. The major contributions of this thesis include:​ (i) development of the relation between foaming process parameters and the generated microcellular structure and morphology, (ii) characterization of the control of the foaming process for the production of acoustical foams with various microcellular structures, (iii) characterization of the effects of the structure and morphology on the acoustical behavior of microcellular foams, (iv) performing theoretical studies on the Effects of the morphological parameters on the acoustical behaviors of foams, and hence, (v) the development of a new corrected sound absorption model that accounts for the morphological and structural factors in acoustical modeling of foams, (vi) the application of the newly developed model to adjust accurately the structure and morphology of microcellular foams and optimize their acoustical performances, and (vii) characterization and modeling of novel acoustical microcellular ceramic foams.