Electrochemical metallization-based two-dimension- al (2D) material memristors with vertical transport and small inter-electrode distances have been reported recently. Their device characteristics exhibit multiple conductance states with relatively low switching voltages, which make them well-suited for low power neuromorphic applications. Our work models the transport in these 2D material-based memristors, with a focus on explaining and capturing their current-voltage characteristics. The model also captures the dynamics of switching (with an emphasis on the estimation of switching energies and delays), and quantitatively captures the experimentally observed spike-time-dependent plasticity behaviour in these devices. The simulation results obtained using our model (and implemented in Verilog-A) have been validated with experimental data from multiple sources. Our work demonstrates the flexibility of including different transport mechanisms (such as, tunneling, space charge limited conduction) in a unified simulation framework. © 2002-2012 IEEE.