Resistive random-access memories (RRAMs) are overwhelmingly viewed as potential candidates for the next generation of non-volatile memory devices. Here, we discuss the advantages of the kinetic Monte Carlo (KMC) simulation framework for RRAMs. We use a robust KMC simulator to analyze transport in promising oxide structures. The simulator couples self-consistently charge transport and thermal effects in the three-dimensional (3D) space, allowing a realistic reconstruction of the conductive filaments responsible for switching. By presenting insightful results, we argue that using a 3D physical electro-thermal simulator is necessary for understanding RRAM operation and reliability. © 2019 IEEE.