Electrostatic
control of charge carrier concentration underlies
the field-effect transistor (FET), which is among the most ubiquitous
devices in the modern world. As transistors and related electronic
devices have been miniaturized to the nanometer scale, electrostatics
have become increasingly important, leading to progressively sophisticated
device geometries such as the finFET. With the advent of atomically
thin materials in which dielectric screening lengths are greater than
device physical dimensions, qualitatively different opportunities
emerge for electrostatic control. In this Review, recent demonstrations
of unconventional electrostatic modulation in atomically thin materials
and devices are discussed. By combining low dielectric screening with
the other characteristics of atomically thin materials such as relaxed
requirements for lattice matching, quantum confinement of charge carriers,
and mechanical flexibility, high degrees of electrostatic spatial
inhomogeneity can be achieved, which enables a diverse range of gate-tunable
properties that are useful in logic, memory, neuromorphic, and optoelectronic
technologies.