When the signal information to be extracted from a particular measurement is complex and severely contaminated with noise, then more information about the underlying physics, measurement dynamics, and noise must be incorporated into the processor. This concept defines the basic model-based approach to signal processing. Here, the development of model-based signal processing techniques applied to a diverse set of acoustic problems is discussed: (1) the extraction of sounds from a prosthetic heart valve for failure detection; (2) the enhancement of laser ultrasonic sounds in materials for nondestructive evaluation; and (3) the extraction of parameters from ocean acoustic measurements for target localization. Recall that model-based signal processing is a well-defined methodology enabling the inclusion of process, measurement, and noise models into sophisticated processing algorithms. The basic principle relies on the notion that the more information incorporated about the physics, measurements, and noise into the processor, the better (smaller error variance) the enhancement. When these parameters exactly ``match'' the process, then minimum variance can be achieved, yielding the best (in a mean-squared sense) possible results. Thus model-based processing finds its roots in minimum variance design where a cost function is investigated until it statistically yields the minimum error between predicted and measured values.