Genomic enhancers are important regulators of gene expression, but their identification is a challenge, and methods depend on indirect measures of activity. We developed a method termed STARR-seq to directly and quantitatively assess enhancer activity for millions of candidates from arbitrary sources of DNA, which enables screens across entire genomes. When applied to the Drosophila genome, STARR-seq identifies thousands of cell type-specific enhancers across a broad continuum of strengths, links differential gene expression to differences in enhancer activity, and creates a genome-wide quantitative enhancer map. This map reveals the highly complex regulation of transcription, with several independent enhancers for both developmental regulators and ubiquitously expressed genes. STARR-seq can be used to identify and quantify enhancer activity in other eukaryotes, including humans.