  We survey some of the recent advances in mean estimation and regression
function estimation. In particular, we describe sub-Gaussian mean estimators
for possibly heavy-tailed data both in the univariate and multivariate
settings. We focus on estimators based on median-of-means techniques but other
methods such as the trimmed mean and Catoni's estimator are also reviewed. We
give detailed proofs for the cornerstone results. We dedicate a section on
statistical learning problems--in particular, regression function
estimation--in the presence of possibly heavy-tailed data.
