  Radio observations of tidal disruption events (TDEs) probe material ejected
by the disruption of stars by supermassive black holes (SMBHs), uniquely
tracing the formation and evolution of jets and outflows, revealing details of
the disruption hydrodynamics, and illuminating the environments around
previously-dormant SMBHs. To date, observations reveal a surprisingly diverse
population. A small fraction of TDEs (at most a few percent) have been observed
to produce radio-luminous mildly relativistic jets. The remainder of the
population are radio quiet, producing less luminous jets, non-relativistic
outflows or, possibly, no radio emission at all. Here, we review the radio
observations that have been made of TDEs to date and discuss possible
explanations for their properties, focusing on detected sources and, in
particular, on the two best-studied events: Sw J1644+57 and ASASSN-14li. We
also discuss what we have learned about the host galaxies of TDEs from radio
observations and review constraints on the rates of bright and faint radio
outflows in TDEs. Upcoming X-ray, optical, near-IR, and radio surveys will
greatly expand the sample of TDEs, and technological advances open the exciting
possibility of discovering a sample of TDEs in the radio band unbiased by host
galaxy extinction.
