The timing of puberty is a highly polygenic childhood trait that is epidemiologically associated with various adult diseases. Using 1000 Genomes Project-imputed genotype data in up to similar to 370,000 women, we identify 389 independent signals (P <5 x 10(-8)) for age at menarche, a milestone in female pubertal development. In Icelandic data, these signals explain similar to 7.4% of the population variance in age at menarche, corresponding to similar to 25% of the estimated heritability. We implicate similar to 250 genes via coding variation or associated expression, demonstrating significant enrichment in neural tissues. Rare variants near the imprinted genes MKRN3 and DLK1 were identified, exhibiting large effects when paternally inherited. Mendelian randomization analyses suggest causal inverse associations, independent of body mass index (BMI), between puberty timing and risks for breast and endometrial cancers in women and prostate cancer in men. In aggregate, our findings highlight the complexity of the genetic regulation of puberty timing and support causal links with cancer susceptibility.