By performing EELS in conjunction with the Z-contrast imaging technique in the scanning transmission electron microscope (STEM), detailed information on the composition, chemistry and structure of materials can be obtained with atomic resolution and sensitivity. This unprecedented resolution can be achieved by using an atomic resolution Z-contrast image to first identify structural features of interest and then to position the electron probe over the feature for spectral acquisition. This method greatly limits the number of spectra that need to be acquired from a given specimen, thus reducing total acquisition time and specimen stability problems. In addition, a key advantage of this methodology is that the collection conditions for the spectrum can be tailored to produce an incoherent, atomic resolution spectrum that can be correlated directly with the image. This means the image can be used as a reference atomic structure for theoretical modeling of the spectral fine-structure. Using multiple scattering analysis, the reference structure can be modified to reproduce the experimental spectrum, thus giving a 3-dimensional structural determination that is sensitive to single atom vacancies and impurities. In this paper, the application of this combined EELS and Z-contrast technique to various materials problems is described. In the case of the MBE growth of CdTe on Si, the combined atomic resolution techniques allow the diffusion of Te into the silicon substrate to be identified and a novel graphoepitaxial growth mechanism to be identified. For nanoscale iron particles used as a fuel additive to reduce/enhance soot formation during combustion, measurement of the distribution of iron oxidation states within the particles permits a mechanism for soot formation to be proposed. The application of the multiple scattering analysis techniques to the study of grain boundaries is described for tilt boundaries in TiO₂ and SrTiO₃. In both cases, the multiple scattering analysis gives information not present in the image and allows the 3-dimensional structure of each boundary to be determined.