Rényi differential privacy is a relaxation of differential privacy based on the Rényi divergence. It provides a more accurate representation of privacy guarantees, especially for composite mechanisms. The paper introduces Rényi differential privacy, which is a stronger privacy definition than $(\epsilon, \delta)$-differential privacy. It allows for tighter analysis of privacy loss and is more suitable for expressing guarantees of privacy-preserving algorithms and for composition of heterogeneous mechanisms. The paper demonstrates that Rényi differential privacy can be reduced to $(\epsilon, \delta)$-differential privacy and proves an advanced composition theorem. It also applies Rényi differential privacy to analyze basic mechanisms such as randomized response, Laplace, and Gaussian noise addition. The paper shows that Rényi differential privacy offers a more accurate and operationally convenient way to track cumulative privacy loss and allows combining the concept of a privacy budget with advanced composition theorems. The paper concludes with open questions about the future of differential privacy.Rényi differential privacy is a relaxation of differential privacy based on the Rényi divergence. It provides a more accurate representation of privacy guarantees, especially for composite mechanisms. The paper introduces Rényi differential privacy, which is a stronger privacy definition than $(\epsilon, \delta)$-differential privacy. It allows for tighter analysis of privacy loss and is more suitable for expressing guarantees of privacy-preserving algorithms and for composition of heterogeneous mechanisms. The paper demonstrates that Rényi differential privacy can be reduced to $(\epsilon, \delta)$-differential privacy and proves an advanced composition theorem. It also applies Rényi differential privacy to analyze basic mechanisms such as randomized response, Laplace, and Gaussian noise addition. The paper shows that Rényi differential privacy offers a more accurate and operationally convenient way to track cumulative privacy loss and allows combining the concept of a privacy budget with advanced composition theorems. The paper concludes with open questions about the future of differential privacy.