Over the past few years graphene has become one the most studied systems in  the field of nanoelectronics. The fact that nanostructured graphene (graphene ribbons, graphene dots, voids in graphene, etc.) can present magnetic order also makes it of interest for spintronic applications. In my talk I will discuss how the associated imbalance in the number of atoms belonging to the two graphene sublattices, the existence of zero-energy states, and the total and local magnetic moments are intimately related. We consider electronic interactions both in a mean-field approximation of the one-orbital Hubbard model and with density functional theory calculations. We find that the magnetic properties of nanometer-sized graphene structures with triangular and hexagonal shapes terminated by zigzag edges happen to be drastically different. We also study the magnetism associated to a single void and the magnetic interactions developed between voids in graphene and graphene ribbons.