The emergence of magnetism in graphene and its nanostructures is a topic of significant interest for future technological applications, particularly in spintronics. This review discusses the various scenarios in which magnetic correlations arise in graphene-based systems, including zero-dimensional nanofragments, one-dimensional nanoribbons, and defect-induced magnetism in graphene and graphite. The physical mechanisms behind these phenomena are illustrated using computational models based on simple Hamiltonians. The review also covers spin transport properties, proposed designs of spintronic devices, and the magnetic ordering at finite temperatures, along with recent experimental achievements. Graphene, a two-dimensional form of carbon, has a unique electronic structure with linear band dispersion at the Fermi level, which leads to novel physical phenomena. While ideal graphene is nonmagnetic, its derivatives and nanostructures can exhibit various magnetic behaviors. The magnetic properties of graphene nanostructures are particularly promising for spintronics, which aims to utilize the spin degree of freedom of electrons for information processing and storage. The first reproducible experimental reports of magnetism in p-block compounds were published in 1991, showing ferromagnetic ordering in certain organic materials. Later, high-temperature ferromagnetism was observed in rhombohedral C60 under high pressure, although the results were later retracted due to concerns about the presence of magnetic impurities. Room-temperature ferromagnetism was also observed in proton-irradiated graphite, which was found to have a graphene-like character. Recent studies have shown that even untreated graphite can exhibit ferromagnetism, possibly due to grain boundaries acting as 2D periodic networks of point defects. Computational approaches, such as the mean-field Hubbard model, are used to study the magnetic properties of graphene. The model considers the interactions between electrons and predicts the onset of magnetism through the Stoner criterion. The results of these models are compared with first-principles calculations, showing good agreement when the parameter U/t is appropriately chosen. The model also predicts the presence of zero-energy states and the total spin of the system, which are important for understanding magnetic properties. The application of counting rules in graphene systems helps predict the number of zero-energy states and the total spin. These rules are applied to small graphene fragments, showing that the magnetic properties depend on the shape and size of the fragments. For example, a hexagonal fragment with equal numbers of sites in sublattices A and B has zero magnetic moment, while a triangular fragment with unequal sublattices has a magnetic moment. The physical mechanism of edge magnetism in graphene nanoribbons is discussed, showing that zigzag edges can exhibit ferromagnetic ordering. The magnetic properties of these nanoribbons are influenced by the width and the application of electric fields, which can induce half-metallicity. The coupling between magnetic edges can be controlled by electron or hole doping, and the magnetic properties can be switched between different states. The review also discusses the potentialThe emergence of magnetism in graphene and its nanostructures is a topic of significant interest for future technological applications, particularly in spintronics. This review discusses the various scenarios in which magnetic correlations arise in graphene-based systems, including zero-dimensional nanofragments, one-dimensional nanoribbons, and defect-induced magnetism in graphene and graphite. The physical mechanisms behind these phenomena are illustrated using computational models based on simple Hamiltonians. The review also covers spin transport properties, proposed designs of spintronic devices, and the magnetic ordering at finite temperatures, along with recent experimental achievements. Graphene, a two-dimensional form of carbon, has a unique electronic structure with linear band dispersion at the Fermi level, which leads to novel physical phenomena. While ideal graphene is nonmagnetic, its derivatives and nanostructures can exhibit various magnetic behaviors. The magnetic properties of graphene nanostructures are particularly promising for spintronics, which aims to utilize the spin degree of freedom of electrons for information processing and storage. The first reproducible experimental reports of magnetism in p-block compounds were published in 1991, showing ferromagnetic ordering in certain organic materials. Later, high-temperature ferromagnetism was observed in rhombohedral C60 under high pressure, although the results were later retracted due to concerns about the presence of magnetic impurities. Room-temperature ferromagnetism was also observed in proton-irradiated graphite, which was found to have a graphene-like character. Recent studies have shown that even untreated graphite can exhibit ferromagnetism, possibly due to grain boundaries acting as 2D periodic networks of point defects. Computational approaches, such as the mean-field Hubbard model, are used to study the magnetic properties of graphene. The model considers the interactions between electrons and predicts the onset of magnetism through the Stoner criterion. The results of these models are compared with first-principles calculations, showing good agreement when the parameter U/t is appropriately chosen. The model also predicts the presence of zero-energy states and the total spin of the system, which are important for understanding magnetic properties. The application of counting rules in graphene systems helps predict the number of zero-energy states and the total spin. These rules are applied to small graphene fragments, showing that the magnetic properties depend on the shape and size of the fragments. For example, a hexagonal fragment with equal numbers of sites in sublattices A and B has zero magnetic moment, while a triangular fragment with unequal sublattices has a magnetic moment. The physical mechanism of edge magnetism in graphene nanoribbons is discussed, showing that zigzag edges can exhibit ferromagnetic ordering. The magnetic properties of these nanoribbons are influenced by the width and the application of electric fields, which can induce half-metallicity. The coupling between magnetic edges can be controlled by electron or hole doping, and the magnetic properties can be switched between different states. The review also discusses the potential