Carbon forms many allotropic forms with different dimensionality : three-dimensional diamond , quasi-two-dimensional graphite , one-dimensional nanotubes and zero-dimensional fullerenes . These materials are well known to exhibit remarkable electronic properties depending on their geometry . There exists another form of carbon material , graphene , which is a monolayer graphite . It was only in 2004 when graphene was experimentally isolated. Among graphene derivatives , graphene nanoribbons constitute a fascinating object due to a rich variety of band gaps , from metals to wide-gap semiconductors . In particular , the half-filled zero-energy states emerge in all zigzag nanoribbons and hence they are metallic . Another basic element of graphene derivatives is a graphene nanodisk . It is a nanometer-scale disk-like material which has a closed edge . They are candidates of future carbon-based nanoelectronics and spintronics alternative to silicon devices . Theoretical studies have shown that magnetism can arise in various situations such as point defects , disorder and reduced dimensionality . Using a mean field Hubbard model , we studied the appearance of magnetic textures in zero-dimensional graphene nanofragments , one-dimensional graphene nanoribbons and bulk graphene . Among nanofragments , triangular shape , bowtie and coronene are studied . We discussed how the shape of these materials , the imbalance in the number of atoms belonging to the graphene sublattices , the existence of zero-energy states and the total and local magnetic moments are related . A vacancy induces around itself a quasilocalized impurity state at the fermi level and leads to formation of local magnetic moments . The emerge of quasilocalized impurity state at the fermi level and local magnetic moments due to point defects and vacancies in armchair nanoribbons and bulk graphene are also studied.A simple set of rules based on Lieb theorem which determines the total spin of a bipartite system described by the Hubbard model applied on these systems and compared with the results of numerical calculations . In graphene nanoribbons with zigzag edges , the spin-polarized state and charge-polarized state due to on-site,U , and nearest neighbor,V , Coulomb repulsions within the extended Hubbard model under the maen field approximation were studed.At the end , we focused on the effects of a model disorder potential(Anderson-type) , and illustrated how density of states of zigzag nanoribbons have been affected . Keywords: Graphene nanofragment , graphene nanoribbon , bulk graphene , spin-polarized state , charge-polarized state , spintronic.