Cosmology with redshift surveys of radio sources

We use the K-z relation for radio galaxies to illustrate why it has proved difficult to obtain definitive cosmological results from studies based entirely on catalogues of the brightest radio sources, e.g. 3C. To improve on this situation we have been undertaking redshift surveys of complete samples drawn from the fainter 6C and 7C radio catalogues. We describe these surveys, and illustrate the new studies they are allowing. We also discuss our `filtered' 6C redshift surveys: these have led to the discovery of a radio galaxy at z=4.4, and are sensitive to similar objects at higher redshift provided the space density of these objects is not declining too rapidly with z. There is currently no direct evidence for a sharp decline in the space density of radio galaxies for z > 4, a result only barely consistent with the observed decline of flat-spectrum radio quasars.