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Memristive devices can offer dynamic behaviour, analogue programmability, and scaling and integration capabilities. As a result, they are of potential use in the development of information processing and storage devices for both conventional and unconventional computing paradigms. Their memristive switching processes originate mainly from the modulation of the number and position of structural defects or compositional impurities—what are commonly referred to as imperfections. While the underlying mechanisms and potential applications of memristors based on traditional bulk materials have been extensively studied, memristors based on van der Waals materials have only been considered more recently. Here we examine imperfection-enabled memristive switching in van der Waals materials. We explore how imperfections— together with the inherent physicochemical properties of the van der Waals materials—create different switching mechanisms, and thus provide a range of opportunities to engineer switching behaviour in memristive devices. We also discuss the challenges involved in terms of material selection, mechanism investigation and switching uniformity control, and consider the potential of van der Waals memristors in system-level implementations of efficient computing technologies.