Two previous papers presented measurements of the properties of a complete radio-selected sample of 59 B2 radio sources with flux densities between 1 and 2 Jy at 0.4 GHz (the '1-Jy' sample). Here, the radio and optical identification data are discussed and interpreted. In order to estimate redshifts from the optical data in Paper II, the magnitude-redshift relations for radio galaxies and quasars in the bright-source sample of Laing, Riley & Longair were examined. For galaxies, this relation is well defined to z ∼ 1 and, for z > 0.3, the mean optical luminosity increases with redshift or radio luminosity, reaching an excess of ∼ 2 mag at z ∼ 1. For quasars, the data are consistent with a non-evolving mean optical luminosity. It is argued that it is appropriate to apply these relationships to the 1-Jy sample. The estimated redshifts are used in conjunction with existing data (mainly from bright-source samples) to examine the space-density evolution of the extragalactic radio-source population. Existing models of the space-density evolution tend to overestimate the space density for z 27 W Hz-1, and quasars appear to occupy the same range of radio luminosity at all redshifts, indicating that the shape of the quasar radio luminosity function may be independent of redshift. With the addition of redshift measurements and further optical identifications, it is likely that new strong constraints will be placed on the form of the radio luminosity function at high redshift. There is weak evidence that the spectra of extended radio sources steepen with increasing radio luminosity in a similar fashion to the correlation found in bright source samples, but only if sources with very steep high-frequency spectra are excluded. © 1984 Royal Astronomical Society. Provided by the NASA Astrophysics Data System.