RRAM technology relying on transitional metal oxides (namely OxRAM) is about to reach the industrial stage. Nevertheless the physical-based understanding of the material and process implications at device and circuit levels is still not completely clear, hindering the full industrial exploitation of the OxRAM technology. In this context, this article presents a multi-scale methodology that connects the microscopic material properties to the electrical behavior of OxRAM devices at the circuit level. Microscopic models describing OxRAM operation (i.e., forming, resistive switching) and variability (e.g., cycle-to-cycle, RTN) will be reviewed and used for the development of compact models that will allow investigating the potential of this technology at the circuit level. An overview of some innovative applications involving OxRAM will be finally presented.