To enable large-scale machine learning in bandwidth-hungry environments such as wireless networks, significant progress has been made recently in designing communication-efficient federated learning algorithms with the aid of communication compression. On the other end, privacy preserving, especially at the client level, is another important desideratum that has not been addressed simultaneously in the presence of advanced communication compression techniques yet. In this paper, we propose a unified framework that enhances the communication efficiency of private federated learning with communication compression. Exploiting both general compression operators and local differential privacy, we first examine a simple algorithm that applies compression directly to differentially-private stochastic gradient descent, and identify its limitations. We then propose a unified framework SoteriaFL for private federated learning, which accommodates a general family of local gradient estimators including popular stochastic variance-reduced gradient methods and the state-of-the-art shifted compression scheme. We provide a comprehensive characterization of its performance trade-offs in terms of privacy, utility, and communication complexity, where SoteriaFL is shown to achieve better communication complexity without sacrificing privacy nor utility than other private federated learning algorithms without communication compression.