We propose a model describing the operations of hafnium oxide-based resistive random access memory (RRAM) devices at the microscopic level. Charge carrier and ion transport are self-consistently described starting from the leakage current in pristine HfO₂. Material structural modifications occurring during the RRAM operations, such as conductive filament (CF) creation and disruption, are accounted for. The model describes the complex processes leading to a formation of the CF and its dependence on both electrical conditions (e.g., current compliance, voltage stress, and temperature) and device characteristics (e.g., electrodes material and dielectric thickness).