Non-volatile resistive switching, also known as memristor(1) effect, where an electric field switches the resistance states of a two-terminal device, has emerged as an important concept in the development of high-density information storage, computing and reconfigurable systems(2-9). The past decade has witnessed substantial advances in non-volatile resistive switching materials such as metal oxides and solid electrolytes. It was long believed that leakage currents would prevent the observation of this phenomenon for nanometre-thin insulating layers. However, the recent discovery of non-volatile resistive switching in two-dimensional monolayers of transition metal dichalcogenide(10,11) and hexagonal boron nitride(12) sandwich structures (also known as atomristors) has refuted this belief and added a new materials dimension owing to the benefits of size scaling(10,13). Here we elucidate the origin of the switching mechanism in atomic sheets using monolayer MoS2 as a model system. Atomistic imaging and spectroscopy reveal that metal substitution into a sulfur vacancy results in a non-volatile change in the resistance, which is corroborated by computational studies of defect structures and electronic states. These findings provide an atomistic understanding of non-volatile switching and open a new direction in precision defect engineering, down to a single defect, towards achieving the smallest memristor for applications in ultra-dense memory, neuromorphic computing and radio-frequency communication systems(2,3,11). A combination of atomistic imaging and spectroscopy reveals that metal substitution into a sulfur vacancy is the underlying mechanism for resistive switching in transition metal dichalcogenide monolayers.