Chronic sleep disturbances, associated with cardiometabolic diseases, psychiatric disorders and all-cause mortality, affect 25-30% of adults worldwide. Although environmental factors contribute substantially to self-reported habitual sleep duration and disruption, these traits are heritable 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).