In robust statistics new procedures which have been derived from theoretical considerations are beginning to find their way into applications. Diagnostics have been designed to supplement standard methodology with both graphical and non-graphical procedures. Many diagnostics, particularly graphical ones, have been generally included in common computing packages. A theoretical basis for some diagnostics methods; however, has been a recent development and is the topic of a large part of this volume. Much of both robust estimation and diagnostics finds its beginnings in the work of John W. Tukey; one of his papers in Part II Graphical Displays for Alternate Regression Fits, contributes to the interplay between the two fields.