Title: FSL: Federated Supermask Learning. Abstract: Federated learning (FL) allows multiple clients with (private) data to collaboratively train a common machine learning model without sharing their private training data. In-the-wild deployment of FL faces two major hurdles: robustness to poisoning attacks and communication efficiency. To address these concurrently, we propose Federated Supermask Learning (FSL). FSL server trains a global subnetwork within a randomly initialized neural network by aggregating local subnetworks of all collaborating clients. FSL clients share local subnetworks in the form of rankings of network edges; more useful edges have higher ranks. By sharing integer rankings, instead of float weights, FSL restricts the space available to craft effective poisoning updates, and by sharing subnetworks, FSL reduces the communication cost of training. We show theoretically and empirically that FSL is robust by design and also significantly communication efficient; all this without compromising clients' privacy. Our experiments demonstrate the superiority of FSL in real-world FL settings; in particular, (1) FSL achieves similar performances as state-of-the-art FedAvg with significantly lower communication costs: for CIFAR10, FSL achieves same performance as Federated Averaging while reducing communication cost by $\sim35\%$. (2) FSL is substantially more robust to poisoning attacks than state-of-the-art robust aggregation algorithms.