This chapter discusses diagnostic tests for sleep-related breathing disorders. Sleep-related breathing disorders (SRBDs), previously called sleep-disordered breathing, is a term used to encompass different types of abnormal breathing during sleep. These disorders may alter the organization and duration of sleep, with consequential daytime symptoms, i.e. excessive daytime sleepiness (EDS) or fatigue, and organ system dysfunction, i.e. cardiovascular or metabolic alterations. The obstructive sleep apnea syndrome (OSAS) is the most frequent SRBD in the population. It is characterized by complete or partial collapse of upper airway during sleep, progressive respiratory efforts during airway obstruction, intermittent hypoxia and fragmented sleep. This chapter also covers the tests for measuring excessive daytime sleepiness, most appropriate diagnostic procedure, preparation of the patient for polygraphy, analysis and interpretative strategies and diagnostic criteria for respiratory events.