Back pain is a common and debilitating disorder with largely unknown underlying biology. Here we report a genome-wide association study of back pain using diagnoses assigned in clinical practice; dorsalgia (119,100 cases, 909,847 controls) and intervertebral disc disorder (IDD) (58,854 cases, 922,958 controls). We identify 41 variants at 33 loci. The most significant association (ORIDD = 0.92, P = 1.6 × 10-39; ORdorsalgia = 0.92, P = 7.2 × 10-15) is with a 3'UTR variant (rs1871452-T) in CHST3, encoding a sulfotransferase enzyme expressed in intervertebral discs. The largest effects on IDD are conferred by rare (MAF = 0.07 - 0.32%) loss-of-function (LoF) variants in SLC13A1, encoding a sodium-sulfate co-transporter (LoF burden OR = 1.44, P = 3.1 × 10-11); variants that also associate with reduced serum sulfate. Genes implicated by this study are involved in cartilage and bone biology, as well as neurological and inflammatory processes.