Very many traditional ‘crystalline’ compounds or line phases are known. Close inspection of a large and ever-increasing number of phases, however, has shown that many do not in fact fit into such a neat strait-jacket and are in fact modulated in one form or another [1]. Themodulations in suchmaterials can be short or long range ordered, have large or small amplitude while the associated occupational and displacive Atomic Modulation Functions (AMF’s) required for complete structural characterization in superspace can be essentially sinusoidal, inherently square wave or saw tooth in form. Whatever the particular characteristics, an understanding of the local crystal chemistry as well as the associated physico-chemical properties of such phases can not be had until suchmodulations are recognized and properly taken into account. The Transmission Electron Microscope (TEM) is an extremely well-adapted instrument for the detection as well as the symmetry and structural characterization of such modulated structures. This is as a result of the sensitivity of electron diffraction to weak subtle features of reciprocal space, the ability to obtain such information from small local regions as well as the capacity to image in various modes with excellent spatial resolution and over a considerable range of temperature. In this contribution, the application of electron diffraction to the study of interface, composite, compositionally and/or displacivelymodulated structures (including hollandites, LaSb2Snx, Sn1-xSb1+x, fresnoites etc) will be discussed. The characteristic diffraction signatures associated with the different types of modulated structure will be highlighted along with the practical application of transmission electron microscopy to problems such as pseudo-symmetry and twinning, to indexation in (3+d)-dimensional superspace and to overall superspace symmetry and structural characterization.