Ultrasound imaging is widely used in clinical settings because of its safe non-ionizing radiation and its low cost. The ultrasound images are generated by performing envelope detection on the backscattered signals. These images show different tissues, organs, and major blood vessels (qualitative information only). In the past three decades however, there has been strong interest in obtaining quantitative information about tissue microstructure by analyzing the backscattered signals rather than using envelope detected data only. The backscattered signals contain information about the size, shape, distribution and mechanical properties of the scatterers within the tissues. These properties can be related to the state of the tissue and may be used to differentiate between healthy and diseased tissue. The tissue microstructure information however, can only be obtained if the total ultrasonic attenuation along the propagation path to the region of interest is accurately compensated. The primary contribution of this thesis is developing two methods for estimating the attenuation along the propagation path. Statistical analysis is performed on each method, and the results are validated using computer simulations and tissue mimicking phantoms. The second contribution is estimating the local ultrasonic attenuation in the cervix of human pregnant patients for the purpose of diagnosing premature delivery. The final contribution is optimizing three common local attenuation estimation algorithms, by using computer simulations and tissue mimicking phantoms.