We measure the radio luminosity function (RLF) of steep-spectrum radio sources using three redshift surveys of flux-limited samples selected at low (151 and 178MHz) radio frequency, low-frequency source counts and the local RLF. The redshift surveys used are the new 7C Redshift Survey (7CRS) and the brighter 3CRR and 6CE surveys totalling 356 sources with virtually complete redshift z information. This yields unprecedented coverage of the radio luminosity versus z plane for steep-spectrum sources, and hence the most accurate measurements of the steep-spectrum RLF yet made. We find that a simple dual-population model for the RLF fits the data well, requiring differential density evolution (with z) for the two populations. The low-luminosity population can be associated with radio galaxies with weak emission lines, and includes sources with both FRI and FRII radio structures; its comoving space density ρ rises by about one dex between z~0 and 1 but cannot yet be meaningfully constrained at higher redshifts. The high-luminosity population can be associated with radio galaxies and quasars with strong emission lines, and consists almost exclusively of sources with FRII radio structure; its ρ rises by nearly three dex between z~0 and 2. These results mirror the situation seen in X-ray and optically selected samples of AGN where: (i) low-luminosity objects exhibit a gradual rise in ρ with z that crudely matches the rises seen in the rates of global star formation and galaxy mergers; and (ii) the density of high-luminosity objects rises much more dramatically. The integrated radio luminosity density of the combination of the two populations is controlled by the value of ρ at the low-luminosity end of the RLF of the high-luminosity population, a quantity which has been directly measured at z~1 by the 7CRS. We argue that robust determination of this quantity at higher redshifts requires a new redshift survey based on a large (~1000 source) sample about five times fainter than the 7CRS.