This communication is to elucidate the state-of-the-art of techniques necessary to gather information on a new class of nanoelectronic devices known as memristors and related resistive switching devices, respectively. Unlike classical microelectronic devices such as transistors, the chemical and structural variations occurring upon switching of memristive devices require cutting-edge electron microscopy techniques. Depending on the switching mechanism, some memristors call for the acquisition of atomically resolved structural data, while others rely on atomistic chemical phenomena requiring the application of advanced X-ray and electron spectroscopy to correlate the real structure with properties. Additionally, understanding resistive switching phenomena also necessitates the application not only of pre-and post-operation analysis, but also during the process of switching. This highly challenging in situ characterization also requires the aforementioned techniques while simultaneously applying an electrical bias. Through this review we aim to give an overview of the possibilities and challenges as well as an outlook onto future developments in the field of nanoscopic characterization of memristive devices.