Electron microscopy has undergone a major revolution in the past few years because of the practical implementation of correctors for the parasitic lens aberrations that otherwise limit resolution. This has been particularly significant for scanning transmission electron microscopy (STEM) and now allows electron beams to be produced with a spot size of well below 1 Å , sufficient to resolve inter-atomic spacings in most crystal structures. This means that the advantages of STEM, relatively straightforward interpretation of images and highly localised analysis through electron energy-loss spectroscopy, can now be applied with atomic resolution to all kinds of materials and nanostructures. As this review shows, this is revolutionising our understanding of functional oxide ceramics, thin films, heterostructures and nanoparticles. This includes quantitative analysis of structures with picometre precision, mapping of electric polarisation at the unit cell scale, and mapping of chemistry and bonding on an atom-by-atom basis. This is also now providing the kind of high quality data that are very complementary to density functional theory (DFT) modelling, and combined DFT/microscopy studies are now providing deep insights into the structure and electronic structure of oxide nanostructures. Finally, some suggestions are made as to the prospects for further advances in our atomistic understanding of such materials as a consequence of recent technical advances in spectroscopy and imaging.