  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 gamma-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
beamforming 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 SKA's 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.
