Sleep breathing disorders represent one of the most important factors that influence prognosis in critical patients, directly as an initial cause or indirect process that deteriorates after admission to the Intensive Care Units. Despite this known association, there is little scientific information in key practical questions. For example, how does one approach and diagnose sleep breathing disorders in critical care medicine? How can one measure these associations in patients under non-invasive and invasive mechanical ventilation? During weaning from mechanical ventilation, extubation process, or prevention extubation failure, and finally, their association with short and long term prognosis in medical and postoperative critically patients. In this scenario, they are of great interest to understand these associations In this book, we analyze the rationale for diagnosis and treatment in critically mechanically ventilated, from non-invasive, invasive and weaning from mechanical ventilation process, treatments, protocols and follow-up patients' recommendations. The high prevalence of sleep breathing disorders, increment critically mechanical ventilated patients, new forms of invasive and non-invasive mechanical ventilation justify as multidisciplinary perspective this book, useful for pulmonologists, critical care and anesthesiologist.