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 (HfO x ) 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.