Nowadays, resistive random-Access memories (RRAMs) are widely considered as the next generation of non-volatile memory devices. Here, we employ a physics-based multi-scale kinetic Monte Carlo simulator to study the microscopic transport properties and characteristics of promising RRAM devices based on transition metal oxides, specifically hafnium oxide (HfOx) based structures. The simulator handles self-consistently electronic charge and thermal transport in the three-dimensional (3D) space, allowing the realistic study of the dynamics of conductive filaments responsible for switching. By presenting insightful results, we argue that using a simulator of a 3D nature, accounting for self-consistent fields and self-heating, is necessary for understanding switching in RRAMs. As an example, we look into the unipolar operation mode, by showing how only the correct inclusion of self-heating allows the proper reconstruction of the switching behaviour. The simulation framework is well-suited for exploring the operation and reliability of RRAMs, providing a reliable computational tool for the optimization of existing device technologies and the path finding and development of new RRAM options. © 2019 IEEE.