The breakdown value is a popular measure of the robustness of an estimator against outlying observations. Roughly
speaking it indicates the smallest fraction of contaminants in a sample that causes the estimator to break down,
that is to take on values that are arbitrarily bad or meaningless. In this paper, we recall the definition of the
finite sample as well as the asymptotic breakdown value of an estimator, and we give several examples of
well-known estimators for location, scatter and regression. We discuss the maximal attainable breakdown values,
and give an overview of high-breakdown estimators that attain this maximal bound. Finally we refer to some issues
in more complex models.