Over the past two or three decades, nanoscience and nanotechnology have clearly established themselves as prominent domains in research in physics, not only because of the innovative concepts and properties that they display but also for their capacity to generate many important applications and commercial developments. As many of these new devices exhibit a range of properties (transport, optical, magnetic, catalysis) which are governed by local structural and electronic configurations, such as coordination and bonding at the atomic level, it is no surprise that new tools of investigation are constantly being developed for imaging, analyzing, understanding and controlling at the relevant scale. Among them, electron microscopy has recently demonstrated its ability to meet many of these requirements. In particular, Å-sized probes are nowadays generated by aberration correctors in a scanning transmission electron microscope (STEM) and they can investigate the electron excitation spectrum of the specimen (through electron energy-loss spectroscopy, EELS) with a typical energy resolution of 0.1–0.3 eV over a broad spectral band from the IR to the X ray domain. In the high energy range, characteristic signals due to the excitation of atomic core levels are quite useful because they identify the atoms in the analyzed volume (which can itself be as small as a single atom) and can therefore deliver atomically-resolved elemental maps. But the pixel-by-pixel recording of the fine structures beyond the characteristic threshold is much more informative and tells us how the excited atom is surrounded by its neighbors, what is its exact structural environment and its charge population. The present review focuses on this particularly exciting field, with a special interest in the types of information accessible and their signature. After summarizing the ingredients required for successful experiments (instrumental as well as theoretical), examples encountered in different situations, in particular in single layers of 2D materials and at the interfaces in oxide heterostructures, will demonstrate the present capabilities of this STEM-EELS technique.