Microporous materials, such as zeolites and aluminophosphates, have many applications as molecular sieves and shape-selective catalysts. This is due to their three-dimensional frameworks, which contain regular pores and channels, to their high acidity, arising from Brønsted and Lewis acid active sites, and to the incorporation of transition metal atoms into framework sites. This review firstly provides an introduction into the nature and properties of these materials, and their important applications; the difficulties in their full characterization and possible methods of elucidating their structures are then outlined; finally, methods of characterization, utilizing 'softer X-rays' are introduced. The first method is the determination of low concentrations of transition metals, incorporated into the frameworks using single crystal anomalous dispersion crystallography; synchrotron radiation is used to tune to the absorption edge of the metal atom in question, in order to change its signal relative to that of the rest of the structure, thereby allowing the pinpointing of its positions and the determination of its concentration at each site in the framework. Secondly, the use of longer wavelengths in powder diffraction studies is described, which, by stretching out the powder pattern, thereby reduces the overlapping of the diffraction peaks, thus allowing the structure to be solved by conventional direct methods. Finally, the use of X-ray absorption spectroscopy to determine the metal incorporation and the nature of coordination at the metal atom sites, in Mn silicalite-1 and FAPO-36, are described.