The occurrence of dual active galactic nuclei (AGN) on scales of a few tens of kpc can be used to study merger-induced accretion on massive black holes (MBHs) and to derive clues on MBH mergers, using dual AGN as a parent population of precursors. We investigate the properties of dual AGN in the cosmological simulation Horizon-AGN. We create catalogs of dual AGN selected with distance and luminosity criteria, plus sub-catalogs where further mass cuts are applied. We divide the sample into dual AGN hosted in different galaxies, on the way to a merger, and into those hosted in one galaxy, after the galaxy merger has happened. We find that the relation between MBH and galaxy mass is similar to that of general AGN population and we compare the properties of dual AGN also with a control sample, discussing differences and similarities in masses and Eddington ratios. The typical mass ratio of galaxy mergers associated to dual AGN is 0.2, with mass loss in the smaller galaxy decreasing the mass ratio as the merger progresses. Between 30 and 80 per cent of dual AGN with separations between 4 and 30 kpc can be matched to an ensuing MBH merger. The dual AGN fraction increases with redshift and with separation threshold, although above 50 kpc the increase of multiple AGN limits that of duals. Multiple AGN are generally associated with massive haloes, and mass loss of satellites shapes the galaxy-halo relation.