We report ab initio results for sub-stoichiometric HfOx with different oxygen vacancy densities, useful in exploring microscopic mechanisms that govern the operation of RRAM devices. We demonstrate that oxygen vacancy filaments are energetically more stable than randomly distributed defects. Furthermore, the stability of the filaments increases with the number of confined oxygen vacancies. Energetic and structural analyses show that bonds between neighboring coordinative unsaturated Hf atoms promote filament stability, and electron trapping, due to electron injection, increases the cohesive energy until the injection is moderate. The highly oxygen deficient configuration of the filaments leads to a substantial lowering of the HfOx band gap, which locally increases the conductivity of the system. Charge injection and electric fields modify the mobility of oxygen ions in the proximity of the filament. The simulations suggest that oxygen ion diffusion can lead to an asymmetric reduction of filament thickness and thus to its progressive disruption where the vacancy cohesion energy is lower.