This paper reviews electrodynamic dust shield (EDS) systems used to mitigate dust adhesion and accumulation on optical elements, such as photovoltaic (PV) panels. The EDS system uses an electrodynamic standing wave or travelling wave, generated by applying a two-phase or multi-phase high voltage to parallel line electrodes, to transport charged particles. After presenting a brief history of the research and development of EDS systems, theoretical and numerical investigations are introduced. They elucidate the mechanism of particle dynamics in the electrodynamic field and predict cleaning performance in low-gravity and low-pressure environments on the Moon and Mars. Subsequently, the paper presents the system configuration, including a cleaner plate and power supply, and fundamental characteristics, including the effects of electrode configuration, applied voltage and frequency, and environmental conditions. It also describes the current status of two primary applications of EDS systems: the cleaning of dust deposited on large-scale PV panels used in solar power generation plants and the cleaning of optical elements, such as PV panels, thermal radiators, lenses, and mirrors mounted on rovers for lunar and Martian exploration. In addition, future challenges are discussed, and other space applications are introduced, such as cleaning of spacesuits, transport and particle-size classification of lunar regolith for the insitu resource utilization, and sampling of regolith and water ice particles on the Moon and asteroids.