Machine Learning models are increasingly used in our daily life. For instance, these models can be used for content recommendation during a purchase or to help doctors while making medical decisions,etc. However, to obtain accurate and useful models, we generally need to train the models with large amount of data. Therefore, several entities with limited datasets may want to collaborate in order to improve their local model accuracy. In traditional machine learning, such collaboration requires to first store all entities’ data on a centralized server before training the model on it. Such data centralization might be problematic when the data are sensitive and data privacy is required. Instead of sharing the training data, Federated Learning shares the model parameters between a server, which plays the role of aggregator, and the participating entities. More specifically, the server sends at each round the global model to some participants (downstream). These participants then update the received model with their local data and sends back the updated gradients’ vector to the server (upstream). The server then aggregates all the participants’ updates to obtain the new global model. This operation is repeated until the global model converges. Although Federated Learning improves both the privacy and the accuracy, it is not perfect. In fact, sharing gradients computed by individual parties can leak information about their private training data. Several recent attacks have demonstrated that a sufficiently skilled adversary, who can capture the model updates (gradients) sent by individual parties, can infer whether a specific record or a group property is present in the dataset of a specific party. Moreover, complete training samples can also be reconstructed purely from the captured gradients. Furthermore, Federated Learning is not only vulnerable to privacy attacks, it is also vulnerable to poisoning attacks which can drastically decrease the model accuracy. Finally, Federated Learning incurs large communication costs during upstream/downstream exchanges between the server and the parties. This can be problematic for applications based on bandwidth and energy-constrained devices, as it is the case for mobile systems, for instance. In this thesis, we first propose three bandwidth efficient schemes to reduce the bandwidth costs up to 99.9%. We then propose differentially private extensions of these schemes which are robust against honest-but- curious adversaries (server or participants) and protect the complete dataset of each participant (participant-level privacy). Moreover, our private solutions outperform standard privacy-preserving Federated Learning schemes in terms of accuracy and/or bandwidth efficiency. Finally, we investigate the robustness of our schemes against security attacks performed by malicious participants and discuss a possible privacy-robustness tradeoff which may spur further research.