The last decade has seen a number of advances in computationally efficient algorithms for statistical methods subject to robustness constraints. An estimator may be robust in a number of different ways: to contamination of the dataset, to heavy-tailed data, or in the sense that it preserves privacy of the dataset. We survey recent results in these areas with a focus on the problem of mean estimation, drawing technical and conceptual connections between the various forms of robustness, showing that the same underlying algorithmic ideas lead to computationally efficient estimators in all these settings.