Chronic sleep disturbances, associated with cardiometabolic diseases, psychiatric disorders and all-cause mortality1, 2, affect 25–30% of adults worldwide3. Although environmental factors contribute substantially to self-reported habitual sleep duration and disruption, these traits are heritable4, 5, 6, 7, 8, 9 and identification of the genes involved should improve understanding of sleep, mechanisms linking sleep to disease and development of new therapies. We report single- and multiple-trait genome-wide association analyses of self-reported sleep duration, insomnia symptoms and excessive daytime sleepiness in the UK Biobank (n = 112,586). We discover loci associated with insomnia symptoms (near MEIS1, TMEM132E, CYCL1 and TGFBI in females and WDR27 in males), excessive daytime sleepiness (near AR–OPHN1) and a composite sleep trait (near PATJ (INADL) and HCRTR2) and replicate a locus associated with sleep duration (at PAX8). We also observe genetic correlation between longer sleep duration and schizophrenia risk (rg = 0.29, P = 1.90 × 10−13) and between increased levels of excessive daytime sleepiness and increased measures for adiposity traits (body mass index (BMI): rg = 0.20, P = 3.12 × 10−9; waist circumference: rg = 0.20, P = 2.12 × 10−7).