Acoustical holography is a relatively new method for imaging which is beginning to emerge as a promising technique for the nonionizing, noninvasive visualization of soft tissue structures in biological subjects. With further improvement it could become a valuable method of visualizing internal organs and soft tissue structures in medical diagnostic imaging. Acoustical holography evolved as a logical extension of the principles of optical holography to sound waves. In this paper the basic principles of acoustical holography are explained in physical terms so that the nonmathematically inclined reader new to the field can obtain a physical understanding of how holography works. Some of the methods which are currently being used successfully to obtain images of biological subjects are described.