Background: Hand grip strength, a simple indicator of muscular strength, has been associated with a range of health conditions, including fractures, disability, cardiovascular disease and premature death risk. Twin studies have suggested a high (50-60%) heritability, but genetic determinants are largely unknown. Aims: In this study, our aim was to study genetic variation associated with muscular strength in a large sample of 334,925 individuals of European descent from the UK Biobank, and to evaluate shared genetic aetiology with and causal effects of grip strength on physical and cognitive health. Methods and Results: In our discovery analysis of 223,315 individuals, we identified 101 loci associated with grip strength at genome-wide significance (P<5e-8). Of these, 64 were associated (P<0.01 and consistent direction) also in the replication dataset (N=111,610). Many of the lead SNPs were located in or near genes known to have a function in developmental disorders (FTO, SLC39A8, TFAP2B, TGFA, CELF1, TCF4, BDNF, FOXP1, KIF1B, ANTXR2), and one of the most significant genes based on a gene-based analysis (ATP2A1) encodes SERCA1, the critical enzyme in calcium uptake to the sarcoplasmic reticulum, which plays a major role in muscle contraction and relaxation. Further, we demonstrated a significant enrichment of gene expression in brain-related transcripts among grip strength associations. Finally, we observed inverse genetic correlations of grip strength with cardiometabolic traits, and positive correlation with parents' age of death and education; and showed that grip strength was causally related to fitness, physical activity and other indicators of frailty, including cognitive performance scores. Conclusions: In our study of over 330,000 individuals from the general population, the genetic findings for hand grip strength suggest an important role of the central nervous system in strength performance. Further, our results indicate that maintaining good muscular strength is important for physical and cognitive performance and healthy aging.