<p>The power and energy consumption of resistive switching devices can be lowered by reducing the dimensions of their active layers. Efforts to push this low-energy switching property to its limits have led to the investigation of active regions made with two-dimensional (2D) layered materials. Despite their small dimensions, 2D layered materials exhibit a rich variety of switching mechanisms, each involving different types of atomic structure reconfiguration. In this Review, we highlight and classify the mechanisms of resistive switching in monolayer and bulk 2D layered materials, with a subsequent focus on those occurring in a monolayer and/or localized to point defects in the crystalline sheet. We discuss the complex energetics involved in these fundamentally defect-assisted processes, including the coexistence of multiple mechanisms and the effects of the contacts used. Examining the highly localized ‘atomristor’-type switching, we provide insights into atomic motions and electronic transport across the metal–2D interfaces underlying their operation. Finally, we discuss progress and our perspective on the challenges associated with the development of 2D resistive switching devices. Promising application areas and material systems are identified and suggested for further research.</p>