Over the last five years hybrid organic-inorganic metal halide perovskites have attracted strong interest in the solar cell community as a result of their high power conversion efficiency and the solid opportunity to realise a low-cost as well as industry-scalable technology. Nevertheless, several aspects of this novel class of materials still need to be explored and the level of our understanding is rapidly and constantly evolving, from month to month. This dissertation reports investigations of perovskite solar cells with a particular focus on their local chemical composition. The analytical characterisation of such devices is very challenging due to the intrinsic instability of the organic component in the nanostructured compounds building up the cell. STEM-EDX (Scanning Transmission Electron Microscopy - Energy Dispersive X-ray spectroscopy) was employed to resolve at the nanoscale the morphology and the elemental composition of the devices. Firstly, a powerful procedure, involving FIB (Focus Ion Beam) sample preparation, the acquisition of STEM-EDX maps and the application of cutting edge post-processing data techniques based on multivariate analysis was developed and tested. The application of this method has drastically improved the quality of the signal that can be extracted from perovskite thin films before the onset of beam-induced transformations. Morphology, composition and interfaces in devices deposited by using different methodologies and external conditions were then explored in detail by combining multiple complementary advanced characterisation tools. The observed variations in the nanostructure of the cells were related to different photovoltaic performance, providing instructive indications for the synthesis and fabrication routes of the devices. Finally, the main degradation processes that affect perovskite solar cells were probed. STEM-EDX was used in conjunction with the application of in situ heating, leading to the direct observation of elemental species migration within the device, reported here for the first time with nanometric spatial resolution. Further analyses, involving a set of experiments aimed to study the effects of air exposure and light soaking on the cells, were designed and performed, providing evidence of the main pathways leading to the drastic drop in the device performance.