GRB-selected galaxies are broadly known to be faint, blue, young, star-forming dwarf galaxies. This insight, however, is based in part on heterogeneous samples of optically selected, lower-redshift galaxies. To study the statistical properties of GRB-selected galaxies we here introduce The Optically Unbiased GRB Host (TOUGH) complete sample of 69 X-ray selected Swift GRB host galaxies spanning the redshift range 0.03-6.30 and summarise the first results of a large observational survey of these galaxies.