With the size of devices continuously shrinking, power consumption has become one of the most critical issues concerning modern integrated circuits, which can be reduced by lowering the power supply voltage (VDD) and subthreshold slope (SS). The realization of the sub-60-mV/dec SS is essential to achieve low-power dissipation. Recently, FET devices that decrease SS by filtering out high-energy electrons to cut off the Boltzmann thermal tail have become a research hot spot. Two methods have been proposed to filter out high-energy electrons to suppress the thermal tail energy distribution. One method is using some “cold” materials as electrodes to realize the cold electron injection such as graphene and other Dirac materials. Another method is designing some novel source structures to enhance the electron tunneling based on energy band engineering theory, such as broken-gap structure, p type-Metal-n type structure, and superlattice structure, etc. In this paper, an overview is given on the FET with cold source (CS) design filtering out the high-energy electrons to realize the lower SS, including the recent progress, future development and prospects.