Robust tools for the imperfect world

Data outliers or other data inhomogeneities lead to a violation of the assumptions of traditional statistical estimators and methods. Robust statistics offers tools that can reliably work with contaminated data. Here, outlier detection methods in low and high dimension, as well as important robust estimators and methods for multivariate data are reviewed, and the most important references to the corresponding literature are provided. Algorithms are discussed, and routines in R are provided, allowing for a straightforward application of the robust methods to real data.