The time domain of the sky has been only sparsely explored, a fact reflected in "time domain astronomy" being recognized in the Astronomy Decadal Survey as one of five science frontier discovery areas. At radio wavelengths, recent discoveries from limited surveys, serendipitous discoveries, and followup from other wavelengths indicate that there is much to be found on timescales from nanoseconds to years and at wavelengths from meters to millimeters. The observations have revealed unexpected phenomena such as rotating radio transients and coherent pulses from brown dwarfs. Additionally, archival studies have found not-yet identified radio transients without optical or high-energy hosts. In addition to the known classes of radio transients, possible other classes of objects include extrapolations from known clases and exotica such as orphan gamma-ray burst afterglows, radio-discovered supernovae, tidally-disrupted stars, flare stars, magnetars, and even transmissions from extraterrestrial civilizations. Over the next decade, meter- and centimeter-wave radio telescopes with improved sensitivity, wider fields of view, and flexible digital signal processing will be able to explore radio transient parameter space more comprehensively and systematically.