More than 800 million people suffer from kidney disease, yet the mechanism of kidney dysfunction is poorly understood. In the present study, we define the genetic association with kidney function in 1.5 million individuals and identify 878 (126 new) loci. We map the genotype effect on the methylome in 443 kidneys, transcriptome in 686 samples and single-cell open chromatin in 57,229 kidney cells. Heritability analysis reveals that methylation variation explains a larger fraction of heritability than gene expression. We present a multi-stage prioritization strategy and prioritize target genes for 87% of kidney function loci. We highlight key roles of proximal tubules and metabolism in kidney function regulation. Furthermore, the causal role of SLC47A1 in kidney disease is defined in mice with genetic loss of Slc47a1 and in human individuals carrying loss-of-function variants. Our findings emphasize the key role of bulk and single-cell epigenomic information in translating genome-wide association studies into identifying causal genes, cellular origins and mechanisms of complex traits.