Robust statistical methods provide understanding of suitable models for data that are contaminated by systematic or random departures. A discussion of the “The Grand Plan” for robust statistics provides a historical context. We start robust data analysis with an introduction to estimates of location, introducing the ideas of breakdown point bdp, the proportion of outlying observations that a particular robust analysis can be expected to adjust for, and of the asymptotic relative efficiency eff, how much information is lost by the robust procedure if the data are not contaminated. As one measure increases, the other decreases. We also introduce robust estimates of scale. In the traditional robust approach, analyses are usually made for one value of bdp or eff. Our book focuses on the monitoring approach to robust statistics in which analyses are performed over a range of values of bdp and eff. For some simple examples, including the transformationTransformation of income data, we compare the information obtained from the traditional static and the dynamic monitoring approaches, the latter providing extra insights into the data. The Grand Plan for the wider application of robust procedures can be realized through the monitoring approach, leading to appreciably more effective data analyses.