Abstract We present the final catalogue of the 2dF QSO Redshift Survey (2QZ), based on Anglo-Australian Telescope 2dF spectroscopic observations of 44 576 colour-selected (ub J r) objects with 18.25 < b J < 20.85 selected from automated plate measurement scans of UK Schmidt Telescope (UKST) photographic plates. The 2QZ comprises 23 338 quasi-stellar objects (QSOs), 12 292 galactic stars (including 2071 white dwarfs) and 4558 compact narrow emission-line galaxies. We obtained a reliable spectroscopic identification for 86 per cent of objects observed with 2dF. We also report on the 6dF QSO Redshift Survey (6QZ), based on UKST 6dF observations of 1564 brighter(16 < b J < 18.25) sources selected from the same photographic input catalogue. In total, we identified 322 QSOs spectroscopically in the 6QZ. The completed 2QZ is, by more than a factor of 50, the largest homogeneous QSO catalogue ever constructed at these faint limits (b J < 20.85) and high QSO surface densities (35 QSOs deg−2). As such, it represents an important resource in the study of the Universe at moderate-to-high redshifts. As an example of the results possible with the 2QZ, we also present our most recent analysis of the optical QSO luminosity function and its cosmological evolution with redshift. For a flat, Ωm= 0.3 and ΩΛ= 0.7, universe, we find that a double power law with luminosity evolution that is exponential in look-back time, τ, of the form L *(z)∝ e6.15τ, equivalent to an e-folding time of 2 Gyr, provides an acceptable fit to the redshift dependence of the QSO LF over the range 0.4 < z < 2.1 and M < −22.5. Evolution described by a quadratic in redshift is also an acceptable fit, with L *(z)∝ 10.