Direct detection of gravitational radiation in the audio band is being pursued with a network of kilometer-scale interferometers (LIGO, Virgo, KAGRA). Several space missions (LISA, DECIGO, BBO) have been proposed to search for sub-Hz radiation from massive astrophysical sources. Here we examine the potential sensitivity of three ground-based detector concepts aimed at radiation in the 0.1 -- 10\,Hz band. We describe the plethora of potential astrophysical sources in this band and make estimates for their event rates and thereby, the sensitivity requirements for these detectors. The scientific payoff from measuring astrophysical gravitational waves in this frequency band is great. Although we find no fundamental limits to the detector sensitivity in this band, the remaining technical limits will be extremely challenging to overcome.

19 pages, 12 figures