Sleep-disordered breathing (SDB), characterized by specific underlying physiological mechanisms, comprises obstructive and central pathophysiology, affects nearly 1 billion individuals worldwide, and is associated with excessive cardiopulmonary morbidity. Strong evidence implicates SDB in cardiac arrhythmogenesis. Immediate consequences of SDB include autonomic nervous system fluctuations, recurrent hypoxia, alterations in carbon dioxide/acid-base status, disrupted sleep architecture, and accompanying increases in negative intrathoracic pressures directly affecting cardiac function. Day-night patterning and circadian biology of SDB-induced pathophysiological sequelae collectively influence the structural and electrophysiological cardiac substrate, thereby creating an ideal milieu for arrhythmogenic propensity. Cohort studies support strong associations of SDB and cardiac arrhythmia, with evidence that discrete respiratory events trigger atrial and ventricular arrhythmic events. Observational studies suggest that SDB treatment reduces atrial fibrillation recurrence after rhythm control interventions. However, high-level evidence from clinical trials that supports a role for SDB intervention on rhythm control is not available. The goals of this scientific statement are to increase knowledge and awareness of the existing science relating SDB to cardiac arrhythmias (atrial fibrillation, ventricular tachyarrhythmias, sudden cardiac death, and bradyarrhythmias), synthesizing data relevant for clinical practice and identifying current knowledge gaps, presenting best practice consensus statements, and prioritizing future scientific directions. Key opportunities identified that are specific to cardiac arrhythmia include optimizing SDB screening, characterizing SDB predictive metrics and underlying pathophysiology, elucidating sex-specific and background-related influences in SDB, assessing the role of mobile health innovations, and prioritizing the conduct of rigorous and adequately powered clinical trials.