Automatic diagnosis of the Sleep Apnea-Hypopnea Syndrome (SAHS) has become an important area of research due to the growing interest in the field of sleep medicine and the costs associated with its manual diagnosis. The increment and heterogeneity of the different techniques, however, make it somewhat difficult to adequately follow the recent developments. A literature review within the area of computer-assisted diagnosis of SAHS has been performed comprising the last 15 years of research in the field. Screening approaches, methods for the detection and classification of respiratory events, comprehensive diagnostic systems, and an outline of current commercial approaches are reviewed. An overview of the different methods is presented together with validation analysis and critical discussion of the current state of the art.