The observing program of the Nordic Near-Earth-Object Network (NEON) accrues knowledge about the physical and dynamical properties of near-Earth objects (NEOs) using state-of-the-art inverse methods. Photometric and astrometric observations are being carried out at the Nordic Optical Telescope. Here, the NEON observations from June 2004–September 2006 are reviewed. Statistical orbital inversion is illustrated by the so-called Volume-of-Variation method. Statistical inversion for spins and shapes is carried using a simple triaxial shape model yielding analytical disk-integrated brightnesses for both Lommel-Seeliger and Lambert scattering laws. The novel approach allows spin-shape error analyses with the help of large numbers of sample solutions. Currently, such spin-shape solutions have been derived for 2002 FF12, 2003 MS2, 2003 RX7, and 2004 HW. For (1862) Apollo, an unambiguous spin-shape solution has been obtained using the conventional, convex inversion method and, for (1685) Toro and (1981) Midas, the conventional method has been applied repeatedly to map the regime of possible solutions.