Abstract: Resistive random access memories are emerging as a new type of memory that has the potential to combine both the speed of volatile and the retention of nonvolatile memories. It operates based on the formation/dissolution of a low-resistivity filament being constituted of either metallic ions or atomic vacancies within an insulating matrix. At present, the mechanisms and the parameters controlling the performances of the device remain unclear. In that respect, first-principles simulations provide useful insights on the atomistic mechanisms, the thermodynamic and kinetics factors that modulate the material conductivity, providing guidance into the engineering of the operation of the device. In this paper, we review the current state-of-the-art knowledge on the atomistic switching mechanisms driving the operation of copper-based conductive bridge RRAM and HfOx valence change RRAM. [GRAPHICS] Conceptual illustration of the RRAM device with the filament formation and disruption during its operation. AE/IM/CE are the active electrode/insulating matrix/counterelectrode. The blue circles represent the conducting defects. (C) 2014 WILEY-VCH Verlag GmbH Co. KGaA, Weinheim