This paper briefly describes the filed of diagnostic radar imaging, and discusses how the techniques of mathematical morphology may be brought to bear on the various forms of data commonly used in it, to accomplish different types of tasks. These tasks include tests of data quality, analyses of clutter and radar parameters, and analyses of scattering centers and the mechanisms that give rise to them. Examples are given of morphological processing that can be performed on raw or reconstructed phase history data, on high resolution range profiles, on single magnitude images or sequences of images, and on images based on the image domain phase. New results are described which suggest that the image phase itself may carry useful information about scattering mechanism types. As this paper shows, mathematical morphology provides a little-utilized, yet rich set of tools for the analysis of shape-related phenomena in diagnostic imaging radar data.