That the conclusion based on a data analysis be robust and stable is not merely a desirable feature, it is essential. To merit this quality label, a conclusion must be supported by strong data-based evidence and not simply be a discovery gleaned from a preconceived model and weakly supported by a part of the data. Robustness in statistics refers to the definition and investigation of procedures that lead to such stability. This article gives a brief overview of the concepts and procedures that are relevant in judging robustness. These have mostly been developed over the last five decades. © 2011 John Wiley & Sons, Inc.