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 nanometer 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 nanoscale – transmission 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 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.