Big Data in context and robustness against heterogeneity

The phrase Big Data has generated substantial current discussion within and outside of the field of statistics. Some personal observations about this phenomenon are discussed. One contribution is to put this set of ideas into a larger historical context. Another is to point out the related important concept of robustness against data heterogeneity, and some earlier methods which had that property, and also to discuss a number of interesting open problems motivated by this concept.