The RNA-guided endonuclease Cas9 is a versatile genome-editing tool with a broad range of applications from therapeutics to functional annotation of genes. Cas9 creates double-strand breaks (DSBs) at targeted genomic loci complementary to a short RNA guide. However, Cas9 can cleave off-target sites that are not fully complementary to the guide, which poses a major challenge for genome editing. Here, we use structure-guided protein engineering to improve the specificity of Streptococcus pyogenes Cas9 (SpCas9). Using targeted deep sequencing and unbiased whole-genome off-target analysis to assess Cas9-mediated DNA cleavage in human cells, we demonstrate that "enhanced specificity" SpCas9 (eSpCas9) variants reduce off-target effects and maintain robust on-target cleavage. Thus, eSpCas9 could be broadly useful for genome-editing applications requiring a high level of specificity.