In the quest for higher performance, the dimensions of field-effect transistors (FETs) continue to decrease. However, the reduction in size of FETs comprising 3D semiconductors is limited by the rate at which heat, generated from static power, is dissipated. The increase in static power and the leakage of current between the source and drain electrodes that causes this increase, are referred to as short-channel effects. In FETs with channels made from 2D semiconductors, leakage current is almost eliminated because all electrons are confined in atomically thin channels and, hence, are uniformly influenced by the gate voltage. In this Review, we provide a mathematical framework to evaluate the performance of FETs and describe the challenges for improving the performances of short-channel FETs in relation to the properties of 2D materials, including graphene, transition metal dichalcogenides, phosphorene and silicene. We also describe tunnelling FETs that possess extremely low-power switching behaviour and explain how they can be realized using heterostructures of 2D semiconductors.