Dysphagia, a widespread clinical condition in the elderly, can lead to malnutrition, aspiration pneumonia, and even death. Swallowing sounds emanate from vibrations that occur during the contraction of muscles in the mouth, pharynx, and laryngeal; the opening or closure of the glottis and esophageal sphincter; or the movement of food particles through the throat during swallowing. The development of wearable sensors, data science, and machine learning has spurred growing attention to the clinical method of monitoring swallowing sounds for accurate dysphagia diagnosis. This review delves into the acoustic theory foundation and the application of swallowing sound signal analysis methods, elucidating their potential clinical value for dysphagia diagnosis and treatment.