Terahertz (THz) radiation source is the key device in the application of THz technology.As a compact and coherent source,THz quantum cascade laser (QCL) in which the optical transition can be tailored by engineering the multiple-quantum-well active layer attracts much interests.Over the past eight years significant theoretical and experimental progress in THz QCL has been made since the first demonstration of THz QCLs in 2002.Theoretically,different designs for the carrier extraction in THz QCLs have been made,such as interminiband transitions,resonant-phonon-assisted intersubband transitions,and bound to continuum transitions.Different theoretical models have been used in the simulation of THz QCLs.Among them,the Monte Carlo (MC) method is thought to be the most suitable.Using the MC method,we can intentionally turn on and off each mechanism to study its influence on the transport properties of the device.