The measurement of acoustic attenuation of soft issue is an important topic in the field of ultra sound tissue characterization. In vitro measurements of tissue attenuation have shown the correlation between this physical parameter and the pathological state of the tissue. Motivated by the clinical indications, many methods for in vivo attenuation estimation have been proposed, both in the time-domain and in the frequency-domain. In this paper, a statistical model describing ultrasound propagation, attenuation, and reflection is presented and the relation between tissue attenuation and the mean echo amplitude is formulated. Based on this analysis, several time-domain methods for in vivo attenuation estimation using the echo amplitude information are reviewed and the difficulties of clinical applications of attenuation estimation as a quantitative method for tissue characterization are also discussed.