Do We Know How to Estimate the Mean?

In this talk I discuss mean estimation based on independent observations, perhaps the most basic problems in statistics. Despite its long history, the subject has attracted a flurry of renewed activity. Motivated by applications in machine learning and data science, the problem has been viewed from new angles both from statistical and computational points of view. We review some recent results on the statistical performance of mean estimators that allow heavy tails and adversarial contamination in the data, focusing on high-dimensional aspects.