We present a theoretical study using density functional calculations of the structural, electronic and magnetic properties of 3d transition metal, noble metal and Zn atoms interacting with carbon monovacancies in graphene. We pay special attention to the electronic and magnetic properties of these substitutional impurities and find that they can be fully understood using a simple model based on the hybridization between the states of the metal atom, particularly the d shell, and the defect levels associated with an unreconstructed D3h carbon vacancy. We identify three different regimes associated with the occupation of different carbon–metal hybridized electronic levels: (i) bonding states are completely filled for Sc and Ti, and these impurities are non-magnetic; (ii) the non-bonding d shell is partially occupied for V, Cr and Mn and, correspondingly, these impurities present large and localized spin moments; (iii) antibonding states with increasing carbon character are progressively filled for Co, Ni, the noble metals and Zn. The spin moments of these impurities oscillate between 0 and 1μB and are increasingly delocalized. The substitutional Zn suffers a Jahn–Teller-like distortion from the C3v symmetry and, as a consequence, has a zero spin moment. Fe occupies a distinct position at the border between regimes (ii) and (iii) and shows a more complex behavior: while it is non-magnetic at the level of generalized gradient approximation (GGA) calculations, its spin moment can be switched on using GGA+U calculations with moderate values of the U parameter.