  The detection of gravitational waves from a neutron star merger, GW170817,
marked the dawn of a new era in time-domain astronomy. Monitoring of the radio
emission produced by the merger, including high-resolution radio imaging,
enabled measurements of merger properties including the energetics and
inclination angle. In this work we compare the capabilities of current and
future gravitational wave facilities to the sensitivity of radio facilities to
quantify the prospects for detecting the radio afterglows of gravitational wave
events. We consider three observing strategies to identify future mergers --
widefield follow-up, targeting galaxies within the merger localisation and deep
monitoring of known counterparts. We find that while planned radio facilities
like the Square Kilometre Array will be capable of detecting mergers at
gigaparsec distances, no facilities are sufficiently sensitive to detect
mergers at the range of proposed third-generation gravitational wave detectors
that would operate starting in the 2030s.
