In order to satisfy the national demands for developing a long-life satellite platform, lunar exploration, and deep-space exploitation, Hall thrusters are now considered the preferred candidate for spacecraft propulsion. A Hall thruster is a type of electric propulsion with an annular structure, in which a propellant, usually xenon, is ionized and then accelerated by electrostatic force to create a propulsive thrust. Low-frequency discharge current oscillations, also called breathing mode oscillations in some references, are among the major research topics of Hall thrusters. Low-frequency oscillations in the range of 10-100 kHz might affect the reliability of power processing unit and reduce the efficiency and specific impulse of Hall thrusters. The control of low-frequency oscillations is an essential challenge in the space application of Hall thrusters. It is proved that the electric field is a highly important influence factor for low-frequency oscillations; therefore, application of a dynamic electric field is a practical way to control low-frequency oscillation.