Transient radio sources are necessarily compact and usually are the locations of explosive or dynamic events, therefore offering unique opportunities for probing fundamental physics and astrophysics. In addition, short-duration transients are powerful probes of intervening media owing to dispersion, scattering and Faraday rotation that modify the signals. While radio astronomy has an impressive record obtaining high time resolution, usually it is achieved in quite narrow fields of view. Consequently, the dynamic radio sky is poorly sampled, in contrast to the situation in the X-ray and γ-ray bands. The SKA has the potential to change this situation, opening up new parameter space in the search for radio transients. We summarize the wide variety of known and hypothesized radio transients and demonstrate that the SKA offers considerable power in exploring this parameter space. Requirements on the SKA to search the parameter space include the abilities to: (1) make targeted searches using beam forming capability; (2) conduct blind, all-sky surveys with dense sampling of the frequency–time plane in wide fields; (3) sample the sky with multiple fields of view from spatially well-separated sites in order to discriminate celestial and terrestrial signals; (4) utilize as much of the SKAs aggregate collecting area as possible in blind surveys, thus requiring a centrally condensed configuration, and; (5) localize repeating transient sources to high angular precision, requiring a configuration with long baselines, thus requiring collecting area in both a centrally condensed “core” array and sufficient area on long baselines.