Background: Sleep-disordered breathing is a common disorder associated with significant morbidity. The genetic architecture of sleep-disordered breathing remains poorly understood. Through the NHLBI Trans-Omics for Precision Medicine (TOPMed) program, we performed the first whole-genome sequence analysis of sleep-disordered breathing. Methods: The study sample was comprised of 7988 individuals of diverse ancestry. Common-variant and pathway analyses included an additional 13,257 individuals. We examined five complementary traits describing different aspects of sleep-disordered breathing: the apnea-hypopnea index, average oxyhemoglobin desaturation per event, average and minimum oxyhemoglobin saturation across the sleep episode, and the percentage of sleep with oxyhemoglobin saturation < 90%. We adjusted for age, sex, BMI, study, and family structure using MMSKAT and EMMAX mixed linear model approaches. Additional bioinformatics analyses were performed with MetaXcan, GIGSEA, and ReMap. Results: We identified a multi-ethnic set-based rare-variant association (p = 3.48 × 10−8) on chromosome X with ARMCX3. Additional rare-variant associations include ARMCX3-AS1, MRPS33, and C16orf90. Novel common-variant loci were identified in the NRG1 and SLC45A2 regions, and previously associated loci in the IL18RAP and ATP2B4 regions were associated with novel phenotypes. Transcription factor binding site enrichment identified associations with genes implicated with respiratory and craniofacial traits. Additional analyses identified significantly associated pathways. Conclusions: We have identified the first gene-based rare-variant associations with objectively measured sleep-disordered breathing traits. Our results increase the understanding of the genetic architecture of sleep-disordered breathing and highlight associations in genes that modulate lung development, inflammation, respiratory rhythmogenesis, and HIF1A-mediated hypoxic response