While federated learning (FL) allows efficient model training with local data at edge devices, among major issues still to be resolved are: slow devices known as stragglers and malicious attacks launched by adversaries. While the presence of both of these issues raises serious concerns in practical FL systems, no known schemes or combinations of schemes effectively address them at the same time. We propose Sageflow, staleness-aware grouping with entropy-based filtering and loss-weighted averaging, to handle both stragglers and adversaries simultaneously. Model grouping and weighting according to staleness (arrival delay) provides robustness against stragglers, while entropy-based filtering and loss-weighted averaging, working in a highly complementary fashion at each grouping stage, counter a wide range of adversary attacks. A theoretical bound is established to provide key insights into the convergence behavior of Sageflow. Extensive experimental results show that Sageflow outperforms various existing methods aiming to handle stragglers/adversaries.