Distributed estimation is a central task in modern data science, where datasets are often generated from distributed sources or are too large to be stored on a centralized machine, and communication is subject to bandwidth and privacy limitations. In this talk, we will consider the problem of estimating high-dimensional distributions and their parameters from distributed samples under communication and differential privacy constraints. We will develop novel encoding and estimation mechanisms that simultaneously achieve optimal privacy and communication efficiency in various canonical settings, including both probabilistic and so called “distribution-free” models. We will investigate both global (worst-case) as well as local complexity of these tasks, where the latter captures the hardness of estimating a specific instance of the problem. We will complement our achievability results with information-theoretic lower bounds that describe how Fisher information from statistical samples scales with privacy and communication constraints. We will conclude by discussing how our theoretical results can be used to improve the experimental performance of federated learning algorithms.