We report the development of physics based models for resistive random-access memory (RRAM) devices. The models are based on a generalized memristive system framework and can explain the dynamic resistive switching phenomena observed in a broad range of devices. Furthermore, by constructing a simple subcircuit, we can incorporate the device models into standard circuit simulators such as SPICE. The SPICE models can accurately capture the dynamic effects of the RRAM devices such as the apparent threshold effect, the voltage dependence of the switching time, and multi-level effects under complex circuit conditions. The device and SPICE models can also be readily expanded to include additional effects related to internal state changes, and will be valuable to help in the design and simulation of memory and logic circuits based on resistive switching devices.