In this review we focus attention on the main methodological approaches for determining and visualizing nanostructural states that can be found in compacted bulk, film, or powder materials. A classification of nanostructural and nanophase materials is discussed. The main methods of structure examination, including direct electron-microscopy studies of nanomaterials, are described. We analyze the fundamental approaches and specific features of the structure and phase nanodiagnostics and describe the main phase, structural, and morphological parameters or properties of the studied materials together with the ways in which they are represented and an estimation of the errors of their determination. The main types of modern transmission and scanning microscopes are considered from the point of view of their technical characteristics and capabilities. The microscopes include attachments for elemental, structural, and texture analyses, as well as for in situ experiments on heating-, cooling-, radiation-, and deformation-induced structural and phase transformations. Various examples of electron microscopy studies of metallic, ceramic, composite, and magnetic materials are given. They were studied by electron diffraction, texture methods, and elemental analyses. The 25-year experience of scientific research performed at Electron Microscopy Center for Collective Use, Institute of Metal Physics, Ural Branch, Russian Academy of Sciences (IMP EMCCU UB RAS), is generalized.