Alzheimer’s disease (AD) is highly heritable and recent studies have identified over 20 disease-associated genomic loci. Yet these only explain a small proportion of the genetic variance, indicating that undiscovered loci remain. Here, we performed a large genome-wide association study of clinically diagnosed AD and AD-by-proxy (71,880 cases, 383,378 controls). AD-by-proxy, based on parental diagnoses, showed strong genetic correlation with AD (r_g = 0.81). Meta-analysis identified 29 risk loci, implicating 215 potential causative genes. Associated genes are strongly expressed in immune-related tissues and cell types (spleen, liver, and microglia). Gene-set analyses indicate biological mechanisms involved in lipid-related processes and degradation of amyloid precursor proteins. We show strong genetic correlations with multiple health-related outcomes, and Mendelian randomization results suggest a protective effect of cognitive ability on AD risk. These results are a step forward in identifying the genetic factors that contribute to AD risk and add novel insights into the neurobiology of AD.