We present new results on the cosmological evolution of unabsorbed (type-1) active galactic nuclei (AGN) selected in the soft (0.5-2 keV) X-ray band. From a variety of ROSAT, XMM-Newton and Chandra surveys we selected a total of ~1000 AGN with an unprecedented spectroscopic and photometric optical/NIR identification completeness. For the first time we are able to derive reliable space densities for low-luminosity (Seyfert-type) X-ray sources at cosmological redshifts. The evolutionary behaviour of AGN shows a strong dependence on X-ray luminosity: while the space density of high-luminosity AGN reaches a peak around z~2, similar to that of optically selected QSO, the space density of low-luminosity AGNs peaks at redshifts below z=1. This confirms previous ROSAT findings of a luminosity-dependent density evolution. Using a rigorous treatment of the optical identification completeness we are able to show that the space density of AGN with X-ray luminosities L_x < 10^45 erg s^-1 declines significantly towards high redshifts.