In recent decades, the association between sleep-disordered breathing (SDB) and cardio- and cerebrovascular diseases (including hypertension, coronary heart disease and stroke) has been the focus of interest of both clinicians and researchers. A growing concern is the increasing prevalence of SDB in the general population, which can be partly explained by the rise in obesity prevalence and population aging, as well as by the development of enhanced diagnostic tools and approaches. Because of evidence of adverse long-term effects of SDB on cardiovascular morbidity and overall mortality, systematic screening for SDB should be considered for populations at risk. The evidence of a long-term benefit of treatment for SDB, however, is still controversial and the best management approaches are still unclear. This article summarises available epidemiological data and focuses on the main pathophysiological mechanisms linking SDB to cardio- and cerebrovascular disorders. We will also give a critical overview of the current diagnostic procedures. The available treatment approaches and their prognostic effects on cardio- and cerebrovascular health will be discussed in a second paper.