Federated learning (FL) is an effective solution to train machine learning models on the increasing amount of data generated by IoT devices and smartphones while keeping such data localized. Most previous work on federated learning assumes that clients operate on static datasets collected before training starts. This approach may be inefficient because 1) it ignores new samples clients collect during training, and 2) it may require a potentially long preparatory phase for clients to collect enough data. Moreover, learning on static datasets may be simply impossible in scenarios with small aggregate storage across devices. It is, therefore, necessary to design federated algorithms able to learn from data streams. In this work, we formulate and study the problem of federated learning for data streams. We propose a general FL algorithm to learn from data streams through an opportune weighted empirical risk minimization. Our theoretical analysis provides insights to configure such an algorithm, and we evaluate its performance on a wide range of machine learning tasks.