With the invention of the electronic stethoscope and other similar recording and data logging devices, acoustic signal processing concepts and methods can now be applied to bowel sounds. In this paper, the literature pertaining to acoustic signal processing for bowel sound analysis is reviewed and discussed. The paper outlines some of the fundamental approaches and machine learning principles that may be used in bowel sound analysis. The advances in signal processing techniques that have allowed useful information to be obtained from bowel sounds from a historical perspective are provided. The document specifically address the progress in bowel sound analysis, such as improved noise reduction, segmentation, signal enhancement, feature extraction, localization of sounds, and machine learning techniques. We have found that advanced acoustic signal processing incorporating novel machine learning methods and artificial intelligence can lead to better interpretation of acoustic information emanating from the bowel.