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: SwJ1644+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.