The crystal structure of *Streptococcus pyogenes* Cas9 in complex with a single guide RNA (sgRNA) and its target DNA is reported at 2.5 Å resolution. The structure reveals a bilobed architecture composed of target recognition and nuclease lobes, which accommodate the sgRNA:DNA heteroduplex in a positively-charged groove. The recognition lobe binds the sgRNA, while the nuclease lobe contains the HNH and RuvC nuclease domains, positioned for cleavage of complementary and non-complementary strands of the target DNA. The PAM-interacting (PI) domain in the nuclease lobe is responsible for PAM recognition. The structure and functional analyses provide insights into the molecular mechanism of RNA-guided DNA targeting by Cas9, facilitating the design of new genome-editing technologies.The crystal structure of *Streptococcus pyogenes* Cas9 in complex with a single guide RNA (sgRNA) and its target DNA is reported at 2.5 Å resolution. The structure reveals a bilobed architecture composed of target recognition and nuclease lobes, which accommodate the sgRNA:DNA heteroduplex in a positively-charged groove. The recognition lobe binds the sgRNA, while the nuclease lobe contains the HNH and RuvC nuclease domains, positioned for cleavage of complementary and non-complementary strands of the target DNA. The PAM-interacting (PI) domain in the nuclease lobe is responsible for PAM recognition. The structure and functional analyses provide insights into the molecular mechanism of RNA-guided DNA targeting by Cas9, facilitating the design of new genome-editing technologies.