The dramatic success of deep learning is largely due to the availability of data. Data samples are often acquired on edge devices, such as smartphones, vehicles, and sensors, and in some cases cannot be shared due to privacy considerations. Federated learning is an emerging machine learning paradigm for training models across multiple edge devices holding local data sets, without explicitly exchanging the data. Learning in a federated manner differs from conventional centralized machine learning and poses several core unique challenges and requirements, which are closely related to classical problems studied in the areas of signal processing and communications.