Triboelectric charging of saltating and colliding sand and dust particles produces strong electric fields in terrestrial dust devils and dust storms. Acceleration of the charged particles, as well as microdischarges between them, generates wideband electromagnetic radiation. Similar phenomena are expected to be ubiquitous on Mars, because Martian dust devils and dust storms are larger, stronger and more frequent than their terrestrial analogues, and electrical discharges occur at a much lower potential gradient in the thin Martian atmosphere. We present theoretical arguments and observational evidence that Martian dust events produce nonthermal wideband electromagnetic radiation detectable from Earth.