Correspondence to: yuchaoyang@pku.edu.cn (Y.Y.), y-taka@ist.hokudai.ac.jp (Y.T.), arita@nano.ist.hokudai.ac.jp (M.A.), m.moors@fz-juelich.de (M.M.), a.kenyon@ucl.ac.uk (A.J.K.)Abstract Memristors or memristive devices are two-terminal nanoionic systems whose resistance switching effects are induced by ion transport and redox reactions in confined spaces down to nanometre or even atomic scales. Understanding such localized and inhomogeneous electrochemical processes is a challenging but crucial task for continued applications of memristors in nonvolatile memory, reconfigurable logic, and brain inspired computing. Here we give a survey for two of the most powerful technologies that are capable of probing the resistance switching mechanisms at the nanoscaletransmission electron microscopy, especially in situ, and scanning tunneling microscopy, for memristive systems based on both electrochemical metallization and valence changes. These studies yield rich information about the size, morphology, composition, chemical state and 2 growth/dissolution dynamics of conducting filaments and even individual metal nanoclusters, and have greatly facilitated the understanding of the underlying mechanisms of memristive switching.Further characterization of cyclic operations leads to additional insights into the degradation in performance, which is important for continued device optimization towards practical applications.Resistive Random Access Memories (ReRAMs), or memristors [1], have tremendous potential for applications in nonvolatile embedded or storage class memories [2, 3], as well as in-memory logic that overcomes the von Neumann bottleneck [4]. They are also envisaged to form the basis of power-efficient neuromorphic systems by implementing plasticity similar to that of biological synapses [5]. Consequently, extensive efforts have been devoted to research into this novel class of devices, including studies of switching materials, device structures, scalability, integration, and so on.In particular, it is very important to understand the fundamental operation mechanisms of ReRAM in order to guide device-related studies. It is well known that the resistance switching effects in memristors are usually modulated by ionic transport and subsequent conducting filament formation/dissolution processes occurring at dimensions around 10 nm, and even down to atomic scales [6][7][8], hence elucidating the switching mechanisms requires advanced characterization techniques capable of resolving the nanoscale switching regions formed randomly in the devices.Here we give a survey of two of the most important technologies in understanding the switching mechanisms of ReRAMtransmission electron microscopy (TEM), especially when applied in situ, and scanning tunneling microscopy (STM). We will discuss the principles and designs behind these techniques, and show how they have furthered the understanding of the nature and dynamic evolution of conductive filaments. Finally, the remaining challenges in the understanding of memristive mechanisms w...