Some aspects of this disclosure provide compositions, methods, and kits for improving the specificity of RNA-programmable endonucleases, such as Cas9. Also provided are variants of Cas9, e.g., Cas9 dimers and fusion proteins, engineered to have improved specificity for cleaving nucleic acid targets. Also provided are compositions, methods, and kits for site-specific nucleic acid modification using Cas9 fusion proteins (e.g., nuclease-inactivated Cas9 fused to a nuclease catalytic domain or a recombinase catalytic domain). Such Cas9 variants are useful in clinical and research settings involving site-specific modification of DNA, for example, genomic modifications.