We present the SWIRE Photometric Redshift Catalogue 1025119 redshifts of unprecedented reliability and of accuracy comparable with or better than previous work. Our methodology is based on fixed galaxy and quasi-stellar object templates applied to data at 0.36-4.5 μm, and on a set of four infrared emission templates fitted to infrared excess data at 3.6-170 μm. The galaxy templates are initially empirical, but are given greater physical validity by fitting star formation histories to them, which also allows us to estimate stellar masses. The code involves two passes through the data, to try to optimize recognition of active galactic nucleus (AGN) dust tori. A few carefully justified priors are used and are the key to supression of outliers. Extinction, AV, is allowed as a free parameter. The full reduced χ2ν (z) distribution is given for each source, so the full error distribution can be used, and aliases investigated. We use a set of 5982 spectroscopic redshifts, taken from the literature and from our own spectroscopic surveys, to analyse the performance of our method as a function of the number of photometric bands used in the solution and the reduced χ2ν. For seven photometric bands (5 optical + 3.6, 4.5 μm), the rms value of (zphot - zspec)/(1 + zspec) is 3.5 per cent, and the percentage of catastrophic outliers [defined as >15 per cent error in (1 + z)], is ~1 per cent. These rms values are comparable with the best achieved in other studies, and the outlier fraction is significantly better. The inclusion of the 3.6- and 4.5-μm IRAC bands is crucial in supression of outliers. We discuss the redshift distributions at 3.6 and 24 μm. In individual fields, structure in the redshift distribution corresponds to clusters which can be seen in the spectroscopic redshift distribution, so the photometric redshifts are a powerful tool for large-scale structure studies. 10 per cent of sources in the SWIRE photometric redshift catalogue have z > 2, and 4 per cent have z > 3, so this catalogue is a huge resource for high-redshift galaxies. A key parameter for understanding the evolutionary status of infrared galaxies is Lir/Lopt. For cirrus galaxies this is a measure of the mean extinction in the interstellar medium of the galaxy. There is a population of ultraluminous galaxies with cool dust and we have shown SEDs for some of the reliable examples. For starbursts, we estimate the specific star formation rate, φ*/M*. Although the very highest values of this ratio tend to be associated with Arp220 starbursts, by no means all ultraluminous galaxies are. We discuss an interesting population of galaxies with elliptical-like spectral energy distributions in the optical and luminous starbursts in the infrared. For dust tori around type 1 AGN, Ltor/Lopt is a measure of the torus covering factor and we deduce a mean covering factor of 40 per cent. Our infrared templates also allow us to estimate dust masses for all galaxies with an infrared excess.